2019 Vol.33(1)
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2019, 33(1): 1-13.
doi: 10.1007/s13344-019-0001-0
Abstract:
In order to account for rigid-flexible coupling effects of floating offshore wind turbines, a nonlinear rigid-flexible coupled dynamic model is proposed in this paper. The proposed nonlinear coupled model takes the higher-order axial displacements into account, which are usually neglected in the conventional linear dynamic model. Subsequently, investigations on the dynamic differences between the proposed nonlinear dynamic model and the linear one are conducted. The results demonstrate that the stiffness of the turbine blades in the proposed nonlinear dynamic model increases with larger overall motions but that in the linear dynamic model declines with larger overall motions. Deformation of the blades in the nonlinear dynamic model is more reasonable than that in the linear model as well. Additionally, more distinct coupling effects are observed in the proposed nonlinear model than those in the linear model. Finally, it shows that the aerodynamic loads, the structural loads and global dynamic responses of floating offshore wind turbines using the nonlinear dynamic model are slightly smaller than those using the linear dynamic model. In summary, compared with the conventional linear dynamic model, the proposed nonlinear coupling dynamic model is a higher-order dynamic model in consideration of the rigid-flexible coupling effects of floating offshore wind turbines, and accord more perfectly with the engineering facts.
In order to account for rigid-flexible coupling effects of floating offshore wind turbines, a nonlinear rigid-flexible coupled dynamic model is proposed in this paper. The proposed nonlinear coupled model takes the higher-order axial displacements into account, which are usually neglected in the conventional linear dynamic model. Subsequently, investigations on the dynamic differences between the proposed nonlinear dynamic model and the linear one are conducted. The results demonstrate that the stiffness of the turbine blades in the proposed nonlinear dynamic model increases with larger overall motions but that in the linear dynamic model declines with larger overall motions. Deformation of the blades in the nonlinear dynamic model is more reasonable than that in the linear model as well. Additionally, more distinct coupling effects are observed in the proposed nonlinear model than those in the linear model. Finally, it shows that the aerodynamic loads, the structural loads and global dynamic responses of floating offshore wind turbines using the nonlinear dynamic model are slightly smaller than those using the linear dynamic model. In summary, compared with the conventional linear dynamic model, the proposed nonlinear coupling dynamic model is a higher-order dynamic model in consideration of the rigid-flexible coupling effects of floating offshore wind turbines, and accord more perfectly with the engineering facts.
2019, 33(1): 14-25.
doi: 10.1007/s13344-019-0002-z
Abstract:
The load and corrosion caused by the harsh marine environment lead to the severe degradation of offshore equipment and to their compromised security and reliability. In the quantitative risk analysis, the failure models are difficult to establish through traditional statistical methods. Hence, the calculation of the occurrence probability of small sample events is often met with great uncertainty. In this study, the Bayesian statistical method is implemented to analyze the oil and gas leakages of FPSO internal turret, which is a typical small sample risk but could lead to severe losses. According to the corresponding failure mechanism, two Bayesian statistical models using the Weibull distribution and logarithmic normal distribution as the population distribution are established, and the posterior distribution of the corresponding parameters is calculated. The optimal Bayesian statistical model is determined according to the Bayesian information criterion and Akaike criterion. On the basis of the determined optimal model, the corresponding reliability index is solved to provide basic data for the subsequent risk assessments of FPSO systems.
The load and corrosion caused by the harsh marine environment lead to the severe degradation of offshore equipment and to their compromised security and reliability. In the quantitative risk analysis, the failure models are difficult to establish through traditional statistical methods. Hence, the calculation of the occurrence probability of small sample events is often met with great uncertainty. In this study, the Bayesian statistical method is implemented to analyze the oil and gas leakages of FPSO internal turret, which is a typical small sample risk but could lead to severe losses. According to the corresponding failure mechanism, two Bayesian statistical models using the Weibull distribution and logarithmic normal distribution as the population distribution are established, and the posterior distribution of the corresponding parameters is calculated. The optimal Bayesian statistical model is determined according to the Bayesian information criterion and Akaike criterion. On the basis of the determined optimal model, the corresponding reliability index is solved to provide basic data for the subsequent risk assessments of FPSO systems.
2019, 33(1): 26-33.
doi: 10.1007/s13344-019-0003-y
Abstract:
Scale effect of ISWs loads on Floating Production Storage and Offloading (FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depth-averaged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model. The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension. Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.
Scale effect of ISWs loads on Floating Production Storage and Offloading (FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depth-averaged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model. The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension. Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.
2019, 33(1): 34-43.
doi: 10.1007/s13344-019-0004-x
Abstract:
A sloshing mitigation concept taking advantage of floating layers of solid foam elements is proposed in the present study. Physical experiments are carried out in a liquid tank to investigate the hydrodynamic mechanism of this concept. Effects of the foam-layer thickness, excitation amplitude, and excitation frequency on the sloshing properties are analyzed in detail. It is found that the floating layers of solid foam elements do not evidently affect the fundamental natural sloshing frequency of the liquid tank evidently among the considered cases. At the resonant condition, the maximum wave height and dynamic pressure are greatly reduced as the foam-layer thickness increases. Higher-order pressure components on the tank side gradually vanish with the increase of the foam-layer thickness. Cases with different excitation amplitudes are also analyzed. The phenomenon is observed when the wave breaking in the tank can be suppressed by solid foam elements.
A sloshing mitigation concept taking advantage of floating layers of solid foam elements is proposed in the present study. Physical experiments are carried out in a liquid tank to investigate the hydrodynamic mechanism of this concept. Effects of the foam-layer thickness, excitation amplitude, and excitation frequency on the sloshing properties are analyzed in detail. It is found that the floating layers of solid foam elements do not evidently affect the fundamental natural sloshing frequency of the liquid tank evidently among the considered cases. At the resonant condition, the maximum wave height and dynamic pressure are greatly reduced as the foam-layer thickness increases. Higher-order pressure components on the tank side gradually vanish with the increase of the foam-layer thickness. Cases with different excitation amplitudes are also analyzed. The phenomenon is observed when the wave breaking in the tank can be suppressed by solid foam elements.
2019, 33(1): 44-56.
doi: 10.1007/s13344-019-0005-9
Abstract:
A numerical study based on a wake oscillator model was conducted to determine the response performance of vortex-induced vibration (VIV) on a long flexible cylinder with pinned-pinned boundary conditions subjected to linear and exponential shear flows. The coupling equations of a structural vibration model and wake oscillator model were solved using a standard central finite difference method of the second order. The VIV response characteristics including the structural displacement, structural frequency, structural wavenumber, standing wave behavior, travelling wave behavior, structural velocity, lift force coefficient and transferred energy from the fluid to the structure with different flow profiles were compared. The numerical results show that the VIV displacement is a combination of standing waves and travelling waves. For linear shear flow, standing waves and travelling waves dominate the VIV response within the low-velocity and high-velocity zones, respectively. The negative values of the transferred energy only occur within the low-velocity zone. However, for exponential shear flow, travelling waves dominate the VIV response and the negative energy occurs along the entire length of the cylinder.
A numerical study based on a wake oscillator model was conducted to determine the response performance of vortex-induced vibration (VIV) on a long flexible cylinder with pinned-pinned boundary conditions subjected to linear and exponential shear flows. The coupling equations of a structural vibration model and wake oscillator model were solved using a standard central finite difference method of the second order. The VIV response characteristics including the structural displacement, structural frequency, structural wavenumber, standing wave behavior, travelling wave behavior, structural velocity, lift force coefficient and transferred energy from the fluid to the structure with different flow profiles were compared. The numerical results show that the VIV displacement is a combination of standing waves and travelling waves. For linear shear flow, standing waves and travelling waves dominate the VIV response within the low-velocity and high-velocity zones, respectively. The negative values of the transferred energy only occur within the low-velocity zone. However, for exponential shear flow, travelling waves dominate the VIV response and the negative energy occurs along the entire length of the cylinder.
2019, 33(1): 57-64.
doi: 10.1007/s13344-019-0006-8
Abstract:
A numerical model of the steel catenary riser (SCR) is built based on the slender rod model. The slender rod model, which describes the behavior of the slender riser in terms of the center line position, can solve the geometrical nonlinearity effectively. In a marine environment, the SCR is under the combined internal flow and external loads, such as wave and current. A general analysis considers only the inertial force and the drag force caused by the wave and current. However, the internal flow has an effect on the SCR; it is essential to explore the dynamic response of the SCR with the internal flow. The SCR also suffers the lift force and the fluctuating drag force because of the current. Finite element method is utilized to solve the motion equations. The effects of the internal flow, wave and current on the dynamic response of the SCR are considered. The results indicate that the increase of the internal flow density leads to the decrease of the displacement of the SCR, while the internal flow velocity has little effect on the SCR. The displacement of the SCR increases with the increase of the wave height and period. And the increasing wave period results in an increase in the vibration period of the SCR. The current velocity changes the displacements of the SCR in x- and z-directions. The vibration frequency of the SCR in y-direction increases with the increase of the current velocity.
A numerical model of the steel catenary riser (SCR) is built based on the slender rod model. The slender rod model, which describes the behavior of the slender riser in terms of the center line position, can solve the geometrical nonlinearity effectively. In a marine environment, the SCR is under the combined internal flow and external loads, such as wave and current. A general analysis considers only the inertial force and the drag force caused by the wave and current. However, the internal flow has an effect on the SCR; it is essential to explore the dynamic response of the SCR with the internal flow. The SCR also suffers the lift force and the fluctuating drag force because of the current. Finite element method is utilized to solve the motion equations. The effects of the internal flow, wave and current on the dynamic response of the SCR are considered. The results indicate that the increase of the internal flow density leads to the decrease of the displacement of the SCR, while the internal flow velocity has little effect on the SCR. The displacement of the SCR increases with the increase of the wave height and period. And the increasing wave period results in an increase in the vibration period of the SCR. The current velocity changes the displacements of the SCR in x- and z-directions. The vibration frequency of the SCR in y-direction increases with the increase of the current velocity.
2019, 33(1): 65-72.
doi: 10.1007/s13344-019-0007-7
Abstract:
When pycnocline thickness of ocean density is relatively small, density stratification can be well represented as a two-layer system. In this article, a depth integrated model of the two-layer fluid with constant density is considered, and a variant of the edge-based non-hydrostatic numerical scheme is formulated. The resulting scheme is very efficient since it resolves the vertical fluid depth only in two layers. Despite using just two layers, the numerical dispersion is shown to agree with the analytical dispersion curves over a wide range of kd, where k is the wave number and d the water depth. The scheme was tested by simulating an interfacial solitary wave propagating over a flat bottom, as well as over a bottom step. On a laboratory scale, the formation of an interfacial wave is simulated, which also shows the interaction of wave with a triangular bathymetry. Then, a case study using the Lombok Strait topography is discussed, and the results show the development of an interfacial wave due to a strong current passing through a sill.
When pycnocline thickness of ocean density is relatively small, density stratification can be well represented as a two-layer system. In this article, a depth integrated model of the two-layer fluid with constant density is considered, and a variant of the edge-based non-hydrostatic numerical scheme is formulated. The resulting scheme is very efficient since it resolves the vertical fluid depth only in two layers. Despite using just two layers, the numerical dispersion is shown to agree with the analytical dispersion curves over a wide range of kd, where k is the wave number and d the water depth. The scheme was tested by simulating an interfacial solitary wave propagating over a flat bottom, as well as over a bottom step. On a laboratory scale, the formation of an interfacial wave is simulated, which also shows the interaction of wave with a triangular bathymetry. Then, a case study using the Lombok Strait topography is discussed, and the results show the development of an interfacial wave due to a strong current passing through a sill.
2019, 33(1): 73-85.
doi: 10.1007/s13344-019-0008-6
Abstract:
This study shows that there are two regions with high trace metal concentrations in the Bohai Bay, China. The numerical hydrodynamic model coupled with geochemical analysis was applied to understand the mass transport and sedimentation in the bay. The modeling results show that the two regions are located within the residual current vortexes. Results from the particle-tracking model indicate that the trace metals released from the land sources enter the regions and take a relatively long residence time in the vortexes. The sediment radionuclide data indicates that the two regions experienced continuous and high sedimentation, and trace metals are prone to deposit in the regions. The correlations among trace metals, residual currents and radionuclides data suggest that the tides are the governing factor controlling the distributions of the trace metals in the bay. The consistence among these results also supports the reliabilities of the numerical simulation results of water and trace metal transport in this study.
This study shows that there are two regions with high trace metal concentrations in the Bohai Bay, China. The numerical hydrodynamic model coupled with geochemical analysis was applied to understand the mass transport and sedimentation in the bay. The modeling results show that the two regions are located within the residual current vortexes. Results from the particle-tracking model indicate that the trace metals released from the land sources enter the regions and take a relatively long residence time in the vortexes. The sediment radionuclide data indicates that the two regions experienced continuous and high sedimentation, and trace metals are prone to deposit in the regions. The correlations among trace metals, residual currents and radionuclides data suggest that the tides are the governing factor controlling the distributions of the trace metals in the bay. The consistence among these results also supports the reliabilities of the numerical simulation results of water and trace metal transport in this study.
2019, 33(1): 86-93.
doi: 10.1007/s13344-019-0009-5
Abstract:
Based on phase focusing theory, focusing waves with different spectral types and breaking severities were generated in a wave flume. The time series of surface elevation fluctuation along the flume were obtained by utilizing 22 wave probes mounted along the mid-stream of the flume. Based on the wave spectrum obtained using fast Fourier transform (FFT), the instability characteristics of the energy spectrum were reported in this paper. By analyzing the variation of total spectral energy, the total spectral energy after wave breaking was found to clearly decrease, and the loss value and ratio gradually increased and tended to stabilize with the enhancement of breaking severity for different spectral types. When wave breaking occurred, the energy loss was primarily in a high-frequency range of f/fp>1.0, and energy gain was primarily in a low-frequency range off/fp<1.0. As the breaking severity increased, the energy gain-loss ratio decreased gradually, which demonstrates that the energy was mostly dissipated. For plunging waves, the energy gain-loss ratio reached 24% for the constant wave steepness (CWS) spectrum, and was slightly larger at approximately 30% for the constant wave amplitude (CWA) spectrum, and was the largest at approximately 42% for the Pierson-Moskowitz (PM) spectrum.
Based on phase focusing theory, focusing waves with different spectral types and breaking severities were generated in a wave flume. The time series of surface elevation fluctuation along the flume were obtained by utilizing 22 wave probes mounted along the mid-stream of the flume. Based on the wave spectrum obtained using fast Fourier transform (FFT), the instability characteristics of the energy spectrum were reported in this paper. By analyzing the variation of total spectral energy, the total spectral energy after wave breaking was found to clearly decrease, and the loss value and ratio gradually increased and tended to stabilize with the enhancement of breaking severity for different spectral types. When wave breaking occurred, the energy loss was primarily in a high-frequency range of f/fp>1.0, and energy gain was primarily in a low-frequency range off/fp<1.0. As the breaking severity increased, the energy gain-loss ratio decreased gradually, which demonstrates that the energy was mostly dissipated. For plunging waves, the energy gain-loss ratio reached 24% for the constant wave steepness (CWS) spectrum, and was slightly larger at approximately 30% for the constant wave amplitude (CWA) spectrum, and was the largest at approximately 42% for the Pierson-Moskowitz (PM) spectrum.
2019, 33(1): 94-102.
doi: 10.1007/s13344-019-0010-z
Abstract:
Liquid sloshing is a common phenomenon in the liquid tanks transportation. Liquid waves lead to fluctuating forces on the tank wall. Uncontrolled fluctuations lead to large forces and momentums. Baffles can control these fluctuations. A numerical method, which has been widely used to model this phenomenon, is Smoothed Particle Hydrodynamics (SPH). The Lagrangian nature of this method makes it suitable for simulating free surface flows. In the present study, an accurate Incompressible Smoothed Particle Hydrodynamics (ISPH) method is developed and improved using the kernel gradient correction tensors, particle shifting algorithms, k–ε turbulence model, and free surface particle detectors. Comparisons with the experimental data approve the ability of the present algorithm for simulating shallow water sloshing. The main aim of this study is to investigate the effects of the vertical baffle on the damping of liquid sloshing. Results show that baffles number has a major role in sloshing fluctuation damping.
Liquid sloshing is a common phenomenon in the liquid tanks transportation. Liquid waves lead to fluctuating forces on the tank wall. Uncontrolled fluctuations lead to large forces and momentums. Baffles can control these fluctuations. A numerical method, which has been widely used to model this phenomenon, is Smoothed Particle Hydrodynamics (SPH). The Lagrangian nature of this method makes it suitable for simulating free surface flows. In the present study, an accurate Incompressible Smoothed Particle Hydrodynamics (ISPH) method is developed and improved using the kernel gradient correction tensors, particle shifting algorithms, k–ε turbulence model, and free surface particle detectors. Comparisons with the experimental data approve the ability of the present algorithm for simulating shallow water sloshing. The main aim of this study is to investigate the effects of the vertical baffle on the damping of liquid sloshing. Results show that baffles number has a major role in sloshing fluctuation damping.
2019, 33(1): 103-113.
doi: 10.1007/s13344-019-0011-y
Abstract:
A comprehensive experimental study was carried out on the regular wave attenuation with a trapezoidal pontoon-type floating breakwater (FB) in deep water. The functionalities of two simple FB geometries consist of a rectangle and a trapezoid with the slope of 60° were investigated under the wave attack. A two-dimensional wave flume was used in the experiment; the incident, transmitted waves, mooring line forces and motion responses of the floating breakwaters were measured. Also the influence of the sea state conditions (incident wave height and wave period) and structural parameters (draught of the structure) were investigated using the trapezoidal FB. Our experimental results indicated that the trapezoidal FB significantly reduced the wave transmission and mooring line force when compared with rectangular FBs. A new formula was developed in order to predict the value of the transmission coefficient in trapezoidal FBs with the slope of 60°. Experimental data showed to be consistent with the results of the formula.
A comprehensive experimental study was carried out on the regular wave attenuation with a trapezoidal pontoon-type floating breakwater (FB) in deep water. The functionalities of two simple FB geometries consist of a rectangle and a trapezoid with the slope of 60° were investigated under the wave attack. A two-dimensional wave flume was used in the experiment; the incident, transmitted waves, mooring line forces and motion responses of the floating breakwaters were measured. Also the influence of the sea state conditions (incident wave height and wave period) and structural parameters (draught of the structure) were investigated using the trapezoidal FB. Our experimental results indicated that the trapezoidal FB significantly reduced the wave transmission and mooring line force when compared with rectangular FBs. A new formula was developed in order to predict the value of the transmission coefficient in trapezoidal FBs with the slope of 60°. Experimental data showed to be consistent with the results of the formula.
2019, 33(1): 114-126.
doi: 10.1007/s13344-019-0012-x
Abstract:
In this paper, we present a numerical simulation of a water jet impacting a new aeronautical material Ti555-03 plate. The Computational Fluid Dynamics (CFD) behavior of the jet is investigated using a FV (Finite Volume) method. The Fluid–Structure Interaction (FSI) is studied using a coupled SPH (Smoothed Particle Hydrodynamics)-FE (Finite Element) method. The jets hit the metal sheet with an initial velocity 500 m/s. Two configurations which differ from each other by the position (angle of inclination) of the plate relatively to the axis of revolution of the jet inlet are investigated in this study. The objective of this study is to predict the impact of the fluid produced at high pressure and high speed especially at the first moment of impact. Numerical simulations are carried out under ABAQUS. We have shown in this study that the inclination of the titanium alloy plate by 45° stimulates the phenomenon of recirculation of water. This affects the velocity profile, turbulence and boundary layers in the impact zone. The stagnation zone and the phenomenon of water recirculation are strongly influenced by the slope of the plate which gives a pressure gradient and displacement very important between the two configurations. Fluctuations of physical variables (displacement and pressure) prove the need for a noise and vibratory study. These predictions will subsequently be used for the modeling of the problem of an orthogonal cut in a high-speed machining process assisted by high-pressure water jet.
In this paper, we present a numerical simulation of a water jet impacting a new aeronautical material Ti555-03 plate. The Computational Fluid Dynamics (CFD) behavior of the jet is investigated using a FV (Finite Volume) method. The Fluid–Structure Interaction (FSI) is studied using a coupled SPH (Smoothed Particle Hydrodynamics)-FE (Finite Element) method. The jets hit the metal sheet with an initial velocity 500 m/s. Two configurations which differ from each other by the position (angle of inclination) of the plate relatively to the axis of revolution of the jet inlet are investigated in this study. The objective of this study is to predict the impact of the fluid produced at high pressure and high speed especially at the first moment of impact. Numerical simulations are carried out under ABAQUS. We have shown in this study that the inclination of the titanium alloy plate by 45° stimulates the phenomenon of recirculation of water. This affects the velocity profile, turbulence and boundary layers in the impact zone. The stagnation zone and the phenomenon of water recirculation are strongly influenced by the slope of the plate which gives a pressure gradient and displacement very important between the two configurations. Fluctuations of physical variables (displacement and pressure) prove the need for a noise and vibratory study. These predictions will subsequently be used for the modeling of the problem of an orthogonal cut in a high-speed machining process assisted by high-pressure water jet.
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