2017 Vol.31(1)
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2017, (1): 1-10.
doi: 10.1007/s13344-017-0001-x
Abstract:
This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×105. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 105, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.
This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×105. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 105, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.
2017, (1): 11-18.
doi: 10.1007/s13344-017-0002-9
Abstract:
Attentions have been increasingly paid to the influence of the corrosion on the ultimate strength of ship structures. In consideration of the random characteristics of the corrosion of ship structures, the method for the ultimate strength analysis of the ship stiffened panel structure subjected to random corrosion degradation is presented. According to the measured corrosion data of the bulk carriers, the distribution characteristics of the corrosion data for the stiffened panel on the midship deck are analyzed, and a random corrosion model is established. The ultimate strength of the corroded stiffened panel is calculated by the nonlinear finite element analysis. The statistical descriptions of the ultimate strength of the corroded stiffened panel are defined through the Monte Carlo simulations. A formula is proposed on the ultimate strength reduction of the stiffened panel as a function of the corrosion volume. The reliability analysis of the ultimate strength of the corroded deck stiffened panel is performed. It shows that both the corrosion data of the deck stiffened panel and the ultimate strength of the random corroded deck stiffened panel follow the log-normal distribution. The ultimate stress ratio of the stiffened panel is inversely proportional to the corrosion volume ratio.
Attentions have been increasingly paid to the influence of the corrosion on the ultimate strength of ship structures. In consideration of the random characteristics of the corrosion of ship structures, the method for the ultimate strength analysis of the ship stiffened panel structure subjected to random corrosion degradation is presented. According to the measured corrosion data of the bulk carriers, the distribution characteristics of the corrosion data for the stiffened panel on the midship deck are analyzed, and a random corrosion model is established. The ultimate strength of the corroded stiffened panel is calculated by the nonlinear finite element analysis. The statistical descriptions of the ultimate strength of the corroded stiffened panel are defined through the Monte Carlo simulations. A formula is proposed on the ultimate strength reduction of the stiffened panel as a function of the corrosion volume. The reliability analysis of the ultimate strength of the corroded deck stiffened panel is performed. It shows that both the corrosion data of the deck stiffened panel and the ultimate strength of the random corroded deck stiffened panel follow the log-normal distribution. The ultimate stress ratio of the stiffened panel is inversely proportional to the corrosion volume ratio.
2017, (1): 19-29.
doi: 10.1007/s13344-017-0003-8
Abstract:
This study describes an automatic berthing system with mooring lines. It is designed to be berthed by using mooring device on the upper deck of a ship. It is to berth once maintaining parallel with the quay by controlling both forward and aft breast lines. Berthing method is used through length adjustment of mooring lines connected between ship and quay by controlling the angular velocity and the torque of hydraulic motor in mooring device. The study is conducted under three changing conditions of draft, such as even-keel, rise of the gravity center and trim to stern. Variables affecting berthing stability are determined based on the control performance of each condition. Bond graphs method is used to model the system. Controller is designed as PID control method of reference-model algorithm. The control program is composed of synchronous control system based on the equations derived with the numerical analysis. The tank test is conducted to verify the usefulness of the control program.
This study describes an automatic berthing system with mooring lines. It is designed to be berthed by using mooring device on the upper deck of a ship. It is to berth once maintaining parallel with the quay by controlling both forward and aft breast lines. Berthing method is used through length adjustment of mooring lines connected between ship and quay by controlling the angular velocity and the torque of hydraulic motor in mooring device. The study is conducted under three changing conditions of draft, such as even-keel, rise of the gravity center and trim to stern. Variables affecting berthing stability are determined based on the control performance of each condition. Bond graphs method is used to model the system. Controller is designed as PID control method of reference-model algorithm. The control program is composed of synchronous control system based on the equations derived with the numerical analysis. The tank test is conducted to verify the usefulness of the control program.
2017, (1): 30-36.
doi: 10.1007/s13344-017-0004-7
Abstract:
To analyze the stress wave propagation associated with the vortex-induced vibration (VIV) of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony's method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the "global" dominating frequencies (poles) shared by those signals. The complex amplitude (residues) corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program (NDP) high mode test data were utilized in the numerical studies, including data sets in both the in-line (IL) and cross-flow (CF) directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.
To analyze the stress wave propagation associated with the vortex-induced vibration (VIV) of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony's method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the "global" dominating frequencies (poles) shared by those signals. The complex amplitude (residues) corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program (NDP) high mode test data were utilized in the numerical studies, including data sets in both the in-line (IL) and cross-flow (CF) directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.
Dynamic Response Analysis of the Equivalent Water Depth Truncated Point of the Catenary Mooring Line
2017, (1): 37-47.
doi: 10.1007/s13344-017-0005-6
Abstract:
The real-time computer-controlled actuators are used to connect the truncated parts of moorings and risers in the active hybrid model testing system. This must be able to work in model-scale real time, based on feedback input from the floater motions. Thus, mooring line dynamics and damping effects are artificially simulated in real time, based on a computer-based model of the problem. In consideration of the nonlinear characteristics of the sea platform catenary mooring line, the equations of the mooring line motion are formulated by using the lumped-mass method and the dynamic response of several points on the mooring line is investigated by the time and frequency domain analysis method. The dynamic response of the representative point on the mooring line is analyzed under the condition of two different corresponding upper endpoint movements namely sine wave excitation and random wave excitation. The corresponding laws of the dynamic response between the equivalent water depth truncated points at different locations and the upper endpoint are obtained, which can provide technical support for further study of the active hybrid model test.
The real-time computer-controlled actuators are used to connect the truncated parts of moorings and risers in the active hybrid model testing system. This must be able to work in model-scale real time, based on feedback input from the floater motions. Thus, mooring line dynamics and damping effects are artificially simulated in real time, based on a computer-based model of the problem. In consideration of the nonlinear characteristics of the sea platform catenary mooring line, the equations of the mooring line motion are formulated by using the lumped-mass method and the dynamic response of several points on the mooring line is investigated by the time and frequency domain analysis method. The dynamic response of the representative point on the mooring line is analyzed under the condition of two different corresponding upper endpoint movements namely sine wave excitation and random wave excitation. The corresponding laws of the dynamic response between the equivalent water depth truncated points at different locations and the upper endpoint are obtained, which can provide technical support for further study of the active hybrid model test.
2017, (1): 48-54.
doi: 10.1007/s13344-017-0006-5
Abstract:
Soft computing tools in the form of combination of multiple nonlinear regression and M5' model tree were used for estimation of overtopping rate at the vertical coastal structures. For reliable and precise estimation of overtopping rate, the experimental data available in the database CLASH were used. The dimensionless overtopping rate was estimated in terms of conventional dimensionless parameters including the relative crest freeboard Rc/Hs, seabed slope tanθ, deep water wave steepness Som, surf similarity ξom and local relative water depth ht/Hs. The accuracy of the new model was compared with other existing models and also evaluated with some field measurements. The results indicated that the model presented in this paper is more accurate than other existing models. With statistical parameters, it is shown that the accuracy of predictions in the new model is better than that of other models.
Soft computing tools in the form of combination of multiple nonlinear regression and M5' model tree were used for estimation of overtopping rate at the vertical coastal structures. For reliable and precise estimation of overtopping rate, the experimental data available in the database CLASH were used. The dimensionless overtopping rate was estimated in terms of conventional dimensionless parameters including the relative crest freeboard Rc/Hs, seabed slope tanθ, deep water wave steepness Som, surf similarity ξom and local relative water depth ht/Hs. The accuracy of the new model was compared with other existing models and also evaluated with some field measurements. The results indicated that the model presented in this paper is more accurate than other existing models. With statistical parameters, it is shown that the accuracy of predictions in the new model is better than that of other models.
2017, (1): 55-62.
doi: 10.1007/s13344-017-0007-4
Abstract:
A hybrid underwater glider Petrel-II has been developed and field tested. It is equipped with an active buoyancy unit and a compact propeller unit. Its working modes have been expanded to buoyancy driven gliding and propeller driven level-flight, which can make the glider work in strong currents, as well as many other complicated ocean environments. Its maximal gliding speed reaches 1 knot and the propelling speed is up to 3 knots. In this paper, a 3D dynamic model of Petrel-II is derived using linear momentum and angular momentum equations. According to the dynamic model, the spiral motion in the underwater space is simulated for the gliding mode. Similarly the cycle motion on water surface and the depth-keeping motion underwater are simulated for the level-flight mode. These simulations are important to the performance analysis and parameter optimization for the Petrel-II underwater glider. The simulation results show a good agreement with field trials.
A hybrid underwater glider Petrel-II has been developed and field tested. It is equipped with an active buoyancy unit and a compact propeller unit. Its working modes have been expanded to buoyancy driven gliding and propeller driven level-flight, which can make the glider work in strong currents, as well as many other complicated ocean environments. Its maximal gliding speed reaches 1 knot and the propelling speed is up to 3 knots. In this paper, a 3D dynamic model of Petrel-II is derived using linear momentum and angular momentum equations. According to the dynamic model, the spiral motion in the underwater space is simulated for the gliding mode. Similarly the cycle motion on water surface and the depth-keeping motion underwater are simulated for the level-flight mode. These simulations are important to the performance analysis and parameter optimization for the Petrel-II underwater glider. The simulation results show a good agreement with field trials.
2017, (1): 63-73.
doi: 10.1007/s13344-017-0008-3
Abstract:
A probabilistic framework for durability assessment of concrete structures in marine environments was proposed in terms of reliability and sensitivity analysis, which takes into account the uncertainties under the environmental, material, structural and executional conditions. A time-dependent probabilistic model of chloride ingress was established first to consider the variations in various governing parameters, such as the chloride concentration, chloride diffusion coefficient, and age factor. Then the Nataf transformation was adopted to transform the non-normal random variables from the original physical space into the independent standard Normal space. After that the durability limit state function and its gradient vector with respect to the original physical parameters were derived analytically, based on which the first-order reliability method was adopted to analyze the time-dependent reliability and parametric sensitivity of concrete structures in marine environments. The accuracy of the proposed method was verified by comparing with the second-order reliability method and the Monte Carlo simulation. Finally, the influences of environmental conditions, material properties, structural parameters and execution conditions on the time-dependent reliability of concrete structures in marine environments were also investigated. The proposed probabilistic framework can be implemented in the decision-making algorithm for the maintenance and repair of deteriorating concrete structures in marine environments.
A probabilistic framework for durability assessment of concrete structures in marine environments was proposed in terms of reliability and sensitivity analysis, which takes into account the uncertainties under the environmental, material, structural and executional conditions. A time-dependent probabilistic model of chloride ingress was established first to consider the variations in various governing parameters, such as the chloride concentration, chloride diffusion coefficient, and age factor. Then the Nataf transformation was adopted to transform the non-normal random variables from the original physical space into the independent standard Normal space. After that the durability limit state function and its gradient vector with respect to the original physical parameters were derived analytically, based on which the first-order reliability method was adopted to analyze the time-dependent reliability and parametric sensitivity of concrete structures in marine environments. The accuracy of the proposed method was verified by comparing with the second-order reliability method and the Monte Carlo simulation. Finally, the influences of environmental conditions, material properties, structural parameters and execution conditions on the time-dependent reliability of concrete structures in marine environments were also investigated. The proposed probabilistic framework can be implemented in the decision-making algorithm for the maintenance and repair of deteriorating concrete structures in marine environments.
2017, (1): 74-78.
doi: 10.1007/s13344-017-0009-2
Abstract:
Many research results show that ocean ambient noise and wind speed are highly relevant, and the surface wind speed can be effectively inverted using ocean noise data. In most deep-sea cases, the ambient noise of medium frequency is mainly determined by the surface wind, and there is a conventional relationship between them. This paper gives an equation which shows this relationship firstly, and then a surface-wind inversion method is proposed. An efficient particle filter is used to estimate the speed distribution, and the results exhibit more focused close to the actual wind speed. The method is verified by the measured noise data, and analysis results showed that this approach can accurately give the trend of sea surface wind speed.
Many research results show that ocean ambient noise and wind speed are highly relevant, and the surface wind speed can be effectively inverted using ocean noise data. In most deep-sea cases, the ambient noise of medium frequency is mainly determined by the surface wind, and there is a conventional relationship between them. This paper gives an equation which shows this relationship firstly, and then a surface-wind inversion method is proposed. An efficient particle filter is used to estimate the speed distribution, and the results exhibit more focused close to the actual wind speed. The method is verified by the measured noise data, and analysis results showed that this approach can accurately give the trend of sea surface wind speed.
2017, (1): 79-90.
doi: 10.1007/s13344-017-0010-9
Abstract:
This article simulates the vortex-induced oscillations of a rigid circular cylinder with elastic support using the new ANSYS CFX rigid body solver. This solver requires no solid mesh to setup FSI (Fluid Structure Interaction) simulation. The two-way case was setup in CFX only. Specific mass of the cylinder and flow conditions were similar to previous experimental data with mass damping parameter equal to 0.04, specific mass of 1 and Reynolds number of 3800. Two dimensional simulations were setup. Both one-degree-of-freedom and two-degree-of-freedom cases were run and results were obtained for both cases with reasonable accuracy as compared with experimental results. Eight-figure XY trajectory and lock-in behavior were clearly captured. The obtained results were satisfactory.
This article simulates the vortex-induced oscillations of a rigid circular cylinder with elastic support using the new ANSYS CFX rigid body solver. This solver requires no solid mesh to setup FSI (Fluid Structure Interaction) simulation. The two-way case was setup in CFX only. Specific mass of the cylinder and flow conditions were similar to previous experimental data with mass damping parameter equal to 0.04, specific mass of 1 and Reynolds number of 3800. Two dimensional simulations were setup. Both one-degree-of-freedom and two-degree-of-freedom cases were run and results were obtained for both cases with reasonable accuracy as compared with experimental results. Eight-figure XY trajectory and lock-in behavior were clearly captured. The obtained results were satisfactory.
2017, (1): 91-97.
doi: 10.1007/s13344-017-0011-8
Abstract:
Vibration in heat exchangers is one of the main problems that the industry has faced over last few decades. Vibration phenomenon in heat exchangers is of major concern for designers and process engineers since it can lead to the tube damage, tube leakage, baffle damage, tube collision damage, fatigue, creep etc. In the present study, vibration response is analyzed on single tube located in the centre of the tube bundle having parallel triangular arrangement (60°) with P/D ratio of 1.44. The experiment is performed for two different flow conditions. This kind of experiment has not been reported in the literature. Under the first condition, the tube vibration response is analyzed when there is no internal flow in the tube and under the second condition, the response is analyzed when the internal tube flow is maintained at a constant value of 0.1 m/s. The free stream shell side velocity ranges from 0.8 m/s to 1.3 m/s, the reduced gap velocity varies from 1.80 to 2.66 and the Reynolds number varies from 44500 to 66000. It is observed that the internal tube flow results in larger vibration amplitudes for the tube than that without internal tube flow. It is also established that over the current range of shell side flow velocity, the turbulence is the dominant excitation mechanism for producing vibration in the tube since the amplitude varies directly with the increase in the shell side velocity. Damping has no significant effect on the vibration behavior of the tube for the current velocity range.
Vibration in heat exchangers is one of the main problems that the industry has faced over last few decades. Vibration phenomenon in heat exchangers is of major concern for designers and process engineers since it can lead to the tube damage, tube leakage, baffle damage, tube collision damage, fatigue, creep etc. In the present study, vibration response is analyzed on single tube located in the centre of the tube bundle having parallel triangular arrangement (60°) with P/D ratio of 1.44. The experiment is performed for two different flow conditions. This kind of experiment has not been reported in the literature. Under the first condition, the tube vibration response is analyzed when there is no internal flow in the tube and under the second condition, the response is analyzed when the internal tube flow is maintained at a constant value of 0.1 m/s. The free stream shell side velocity ranges from 0.8 m/s to 1.3 m/s, the reduced gap velocity varies from 1.80 to 2.66 and the Reynolds number varies from 44500 to 66000. It is observed that the internal tube flow results in larger vibration amplitudes for the tube than that without internal tube flow. It is also established that over the current range of shell side flow velocity, the turbulence is the dominant excitation mechanism for producing vibration in the tube since the amplitude varies directly with the increase in the shell side velocity. Damping has no significant effect on the vibration behavior of the tube for the current velocity range.
2017, (1): 98-102.
doi: 10.1007/s13344-017-0012-7
Abstract:
The homotopy method is utilized in the present inverse hull design problem to minimize the wave-making coefficient of a 1300 TEU container ship with a bulbous bow. Moreover, in order to improve the computational efficiency of the algorithm, a properly smooth function is employed to update the homotopy parameter during iteration. Numerical results show that the homotopy method has been successfully applied in the inverse design of the ship hull. This method has an advantage of high performance on convergence and it is credible and valuable for engineering practice.
The homotopy method is utilized in the present inverse hull design problem to minimize the wave-making coefficient of a 1300 TEU container ship with a bulbous bow. Moreover, in order to improve the computational efficiency of the algorithm, a properly smooth function is employed to update the homotopy parameter during iteration. Numerical results show that the homotopy method has been successfully applied in the inverse design of the ship hull. This method has an advantage of high performance on convergence and it is credible and valuable for engineering practice.
2017, (1): 103-113.
doi: 10.1007/s13344-017-0013-6
Abstract:
In order to study the properties of sound-speed dispersion in a sandy sediment, the sound speed was measured both at high frequency (90-170 kHz) and low frequency (0.5-3 kHz) in laboratory environments. At high frequency, a sampling measurement was conducted with boiled and uncooked sand samples collected from the bottom of a large water tank. The sound speed was directly obtained through transmission measurement using single source and single hydrophone. At low frequency, an in situ measurement was conducted in the water tank, where the sandy sediment had been homogeneously paved at the bottom for a long time. The sound speed was indirectly inverted according to the traveling time of signals received by three buried hydrophones in the sandy sediment and the geometry in experiment. The results show that the mean sound speed is approximate 1710-1713 m/s with a weak positive gradient in the sand sample after being boiled (as a method to eliminate bubbles as much as possible) at high frequency, which agrees well with the predictions of Biot theory, the effective density fluid model (EDFM) and Buckingham's theory. However, the sound speed in the uncooked sandy sediment obviously decreases (about 80%) both at high frequency and low frequency due to plenty of bubbles in existence. And the sound-speed dispersion performs a weak negative gradient at high frequency. Finally, a water-unsaturated Biot model is presented for trying to explain the decrease of sound speed in the sandy sediment with plenty of bubbles.
In order to study the properties of sound-speed dispersion in a sandy sediment, the sound speed was measured both at high frequency (90-170 kHz) and low frequency (0.5-3 kHz) in laboratory environments. At high frequency, a sampling measurement was conducted with boiled and uncooked sand samples collected from the bottom of a large water tank. The sound speed was directly obtained through transmission measurement using single source and single hydrophone. At low frequency, an in situ measurement was conducted in the water tank, where the sandy sediment had been homogeneously paved at the bottom for a long time. The sound speed was indirectly inverted according to the traveling time of signals received by three buried hydrophones in the sandy sediment and the geometry in experiment. The results show that the mean sound speed is approximate 1710-1713 m/s with a weak positive gradient in the sand sample after being boiled (as a method to eliminate bubbles as much as possible) at high frequency, which agrees well with the predictions of Biot theory, the effective density fluid model (EDFM) and Buckingham's theory. However, the sound speed in the uncooked sandy sediment obviously decreases (about 80%) both at high frequency and low frequency due to plenty of bubbles in existence. And the sound-speed dispersion performs a weak negative gradient at high frequency. Finally, a water-unsaturated Biot model is presented for trying to explain the decrease of sound speed in the sandy sediment with plenty of bubbles.
2017, (1): 114-122.
doi: 10.1007/s13344-017-0014-5
Abstract:
Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line (IL) vortex-induced vibrations (VIV) analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.
Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line (IL) vortex-induced vibrations (VIV) analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.
2017, (1): 123-129.
doi: 10.1007/s13344-017-0015-4
Abstract:
A control scheme named the variable-lateral-force cavitator, which is focused on the control of lift force, drag force and lateral forces for underwater supercavity vehicles was proposed, and the supercavitating flow around the cavitator was investigated numerically using the mixture multiphase flow model. It is verified that the forces of pitching, yawing, drag and lift, as well as the supercavity size of the underwater vehicle can be effectively regulated through the movements of the control element of the variable-lateral-force cavitator in the radial and circumferential directions. In addition, if the control element on either side protrudes to a height of 5% of the diameter of the front cavitator, an amount of forces of pitching and yawing equivalent to 30% of the drag force will be produced, and the supercavity section appears concave inwards simultaneously. It is also found that both the drag force and lift force of the variable-lateral-force cavitator decline as the angle of attack increases.
A control scheme named the variable-lateral-force cavitator, which is focused on the control of lift force, drag force and lateral forces for underwater supercavity vehicles was proposed, and the supercavitating flow around the cavitator was investigated numerically using the mixture multiphase flow model. It is verified that the forces of pitching, yawing, drag and lift, as well as the supercavity size of the underwater vehicle can be effectively regulated through the movements of the control element of the variable-lateral-force cavitator in the radial and circumferential directions. In addition, if the control element on either side protrudes to a height of 5% of the diameter of the front cavitator, an amount of forces of pitching and yawing equivalent to 30% of the drag force will be produced, and the supercavity section appears concave inwards simultaneously. It is also found that both the drag force and lift force of the variable-lateral-force cavitator decline as the angle of attack increases.
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