2023 Vol.37(1)
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2023, 37(1): 1-15.
doi: 10.1007/s13344-023-0001-y
Abstract:
Experiments were conducted on risers with different mass ratios to study the effect of mode conversion and spanwise correlation. The slenderness ratio of the riser model was set as 169, and the Reynolds numbers are 1600−14400. The dynamic responses of riser models versus reduced velocity were analyzed, and the spanwise displacement, frequency, and trajectory of the mode conversion from the lower to the higher mode were explored. The results revealed that the riser model with a higher mass ratio excites a higher number of modes. The conversion region of multi-mode competition exists and narrows with the increasing mass ratio. Mode conversion is continuous and manifests as the transmission of peaks and troughs in mode shape: the peaks and troughs of mode shape move up in the mode stable development region and move down in the mode conversion region. The single-mode dominating vibration exhibits a standing wave feature, and the traveling wave feature is significant in the mode conversion region. Furthermore, the frequency jump is always transmitted from the trough to the peak of the mode shape, and finally, all the axial positions vibrate at the same frequency. The trajectory in the mode conversion region deviates from the 8-shape and recovers the standard 8-shape at the middle and late stages of the mode stable development region.
Experiments were conducted on risers with different mass ratios to study the effect of mode conversion and spanwise correlation. The slenderness ratio of the riser model was set as 169, and the Reynolds numbers are 1600−14400. The dynamic responses of riser models versus reduced velocity were analyzed, and the spanwise displacement, frequency, and trajectory of the mode conversion from the lower to the higher mode were explored. The results revealed that the riser model with a higher mass ratio excites a higher number of modes. The conversion region of multi-mode competition exists and narrows with the increasing mass ratio. Mode conversion is continuous and manifests as the transmission of peaks and troughs in mode shape: the peaks and troughs of mode shape move up in the mode stable development region and move down in the mode conversion region. The single-mode dominating vibration exhibits a standing wave feature, and the traveling wave feature is significant in the mode conversion region. Furthermore, the frequency jump is always transmitted from the trough to the peak of the mode shape, and finally, all the axial positions vibrate at the same frequency. The trajectory in the mode conversion region deviates from the 8-shape and recovers the standard 8-shape at the middle and late stages of the mode stable development region.
2023, 37(1): 16-28.
doi: 10.1007/s13344-023-0002-x
Abstract:
A novel expandable conductor was designed and applied in deep-water drilling to improve the vertical and lateral bearing capacity with a significant reduction of conductor jetting depth and soaking time. The vertical and lateral bearing capability of expandable conductors was depicted based on the ultimate subgrade reaction method and pile foundation bearing theory. The load-bearing characteristics of a laboratory-scale expandable conductor were analyzed through laboratory experiments. The serial simulation experiments are accomplished to study the bearing characteristics (vertical ultimate bearing capacity, lateral soil pressure, and lateral displacement) during the conductor soaking process. The laboratory experimental results show that the larger the length and thickness of expandable materials are, the higher the bearing capacity of the wellhead will be. During the conductor soaking process, the soil pressure around the three expandable conductors increases faster, strings representing a stronger squeezing effect and resulting in higher vertical bearing capacity. Furthermore, the lateral displacement of novel expandable conductor is smaller than that of the conventional conductor. All the advantages mentioned above contributed to the reduction of conductor’s jetting depth and soaking time. Lastly, the application workflow of a novel expandable deep-water drilling conductor was established and the autonomous expandable conductor was successfully applied in the South China Sea with a significant reduction of conductor’s jetting depth and soaking time. According to the soil properties and designed installation depth of the surface conductor, the arrangement of expandable materials should be designed reasonably to meet the safety condition and reduce the construction cost of the subsea wellhead.
A novel expandable conductor was designed and applied in deep-water drilling to improve the vertical and lateral bearing capacity with a significant reduction of conductor jetting depth and soaking time. The vertical and lateral bearing capability of expandable conductors was depicted based on the ultimate subgrade reaction method and pile foundation bearing theory. The load-bearing characteristics of a laboratory-scale expandable conductor were analyzed through laboratory experiments. The serial simulation experiments are accomplished to study the bearing characteristics (vertical ultimate bearing capacity, lateral soil pressure, and lateral displacement) during the conductor soaking process. The laboratory experimental results show that the larger the length and thickness of expandable materials are, the higher the bearing capacity of the wellhead will be. During the conductor soaking process, the soil pressure around the three expandable conductors increases faster, strings representing a stronger squeezing effect and resulting in higher vertical bearing capacity. Furthermore, the lateral displacement of novel expandable conductor is smaller than that of the conventional conductor. All the advantages mentioned above contributed to the reduction of conductor’s jetting depth and soaking time. Lastly, the application workflow of a novel expandable deep-water drilling conductor was established and the autonomous expandable conductor was successfully applied in the South China Sea with a significant reduction of conductor’s jetting depth and soaking time. According to the soil properties and designed installation depth of the surface conductor, the arrangement of expandable materials should be designed reasonably to meet the safety condition and reduce the construction cost of the subsea wellhead.
2023, 37(1): 29-41.
doi: 10.1007/s13344-023-0003-9
Abstract:
Evaluation of abandonment and recovery operation of steel lazy-wave riser in deepwater is presented in this paper. The calculation procedure includes two single continuous SLWR and cable segments, which are coupled together to form the overall mathematical model. Then the equilibrium equations of SLWR and cable are established based on minimum total potential energy principle. The coupled equations are discretized by the finite difference method and solved by Newton-Raphson technique in an iterative manner. The present method is validated by well-established commercial code OrcaFlex. Recovery methods by considering different ratios of vessel’s moving velocity to cable’s recovery velocity are evaluated to optimize the abandonment and recovery operation. In order to keep the tension more stable during the recovery process, the rate ratio before leaving the seabed is increased, and the rate ratio after leaving the seabed is reduced.
Evaluation of abandonment and recovery operation of steel lazy-wave riser in deepwater is presented in this paper. The calculation procedure includes two single continuous SLWR and cable segments, which are coupled together to form the overall mathematical model. Then the equilibrium equations of SLWR and cable are established based on minimum total potential energy principle. The coupled equations are discretized by the finite difference method and solved by Newton-Raphson technique in an iterative manner. The present method is validated by well-established commercial code OrcaFlex. Recovery methods by considering different ratios of vessel’s moving velocity to cable’s recovery velocity are evaluated to optimize the abandonment and recovery operation. In order to keep the tension more stable during the recovery process, the rate ratio before leaving the seabed is increased, and the rate ratio after leaving the seabed is reduced.
2023, 37(1): 42-52.
doi: 10.1007/s13344-023-0004-8
Abstract:
The carcass layer of flexible pipe comprises a large-angle spiral structure with a complex interlocked stainless steel cross-section profile, which is mainly used to resist radial load. With the complex structure of the carcass layer, an equivalent simplified model is used to study the mechanical properties of the carcass layer. However, the current equivalent carcass model only considers the elastic deformation, and this simplification leads to huge errors in the calculation results. In this study, radial compression experiments were carried out to make the carcasses to undergo plastic deformation. Subsequently, a residual neural network based on the experimental data was established to predict the load−displacement curves of carcasses with different inner diameter in plastic states under radial compression. The established neural network model’s high precision was verified by experimental data, and the influence of the number of input variables on the accuracy of the neural network was discussed. The conclusion shows that the residual neural network model established based on the experimental data of the small-diameter carcass layer can predict the load−displacement curve of the large-diameter carcass layer in the plastic stage. With the decrease of input data, the prediction accuracy of residual network model in plasticity stage will decrease.
The carcass layer of flexible pipe comprises a large-angle spiral structure with a complex interlocked stainless steel cross-section profile, which is mainly used to resist radial load. With the complex structure of the carcass layer, an equivalent simplified model is used to study the mechanical properties of the carcass layer. However, the current equivalent carcass model only considers the elastic deformation, and this simplification leads to huge errors in the calculation results. In this study, radial compression experiments were carried out to make the carcasses to undergo plastic deformation. Subsequently, a residual neural network based on the experimental data was established to predict the load−displacement curves of carcasses with different inner diameter in plastic states under radial compression. The established neural network model’s high precision was verified by experimental data, and the influence of the number of input variables on the accuracy of the neural network was discussed. The conclusion shows that the residual neural network model established based on the experimental data of the small-diameter carcass layer can predict the load−displacement curve of the large-diameter carcass layer in the plastic stage. With the decrease of input data, the prediction accuracy of residual network model in plasticity stage will decrease.
2023, 37(1): 53-61.
doi: 10.1007/s13344-023-0005-7
Abstract:
System identification is a quintessential measure for real-time analysis on kinematic characteristics for deep-sea mining vehicle, and thus to enhance the control performance and testing efficiency. In this study, the system identification algorithm, recursive least square method with instrumental variables (IV-RLS), is tailored to model ‘Pioneer I’, a deep-sea mining vehicle which recently completed a 1305-meter-deep sea trial in the Xisha area of the South China Sea in August, 2021. The algorithm operates on the sensor data collected from the trial to obtain the vehicle’s kinematic model and accordingly design the parameter self-tuning controller. The performances demonstrate the accuracy of the model, and prove its generalization capability. With this model, the optimal controller has been designed, the control parameters have been self-tuned, and the response time and robustness of the system have been optimized, which validates the high efficiency on digital modelling for precision control of deep-sea mining vehicles.
System identification is a quintessential measure for real-time analysis on kinematic characteristics for deep-sea mining vehicle, and thus to enhance the control performance and testing efficiency. In this study, the system identification algorithm, recursive least square method with instrumental variables (IV-RLS), is tailored to model ‘Pioneer I’, a deep-sea mining vehicle which recently completed a 1305-meter-deep sea trial in the Xisha area of the South China Sea in August, 2021. The algorithm operates on the sensor data collected from the trial to obtain the vehicle’s kinematic model and accordingly design the parameter self-tuning controller. The performances demonstrate the accuracy of the model, and prove its generalization capability. With this model, the optimal controller has been designed, the control parameters have been self-tuned, and the response time and robustness of the system have been optimized, which validates the high efficiency on digital modelling for precision control of deep-sea mining vehicles.
2023, 37(1): 62-72.
doi: 10.1007/s13344-023-0006-6
Abstract:
Recent offshore oil and gas loading facilities developed in the Arctic area have led to a considerable awareness of the iceberg draft approximation, where deep keel icebergs may gouge the ocean floor, and these submarine infrastructures would be damaged in the shallower waters. Developing reliable solutions to estimate the iceberg draft requires a profound understanding of the problem’s dominant parameters. As such, the dimensionless groups of the parameters affecting the iceberg draft estimation were determined for the first time in the present study. Using the dimensionless groups recognized and the linear regression (LR) analysis, nine LR models (i.e., LR 1 to LR 9) were developed and then validated using a comprehensive dataset, which has been constructed in this study. A sensitivity analysis distinguished the premium LR models and important dimensionless groups. The best LR model, as a function of all dimensionless parameters, was able to estimate the iceberg draft with the highest level of precision and correlation along with the lowest degree of complexity. The ratio of iceberg length to iceberg height as the “iceberg length ratio” and the ratio of iceberg width to iceberg height as the “iceberg width ratio” was detected as the important dimensionless groups in the estimation of the iceberg draft. An uncertainty analysis demonstrated that the best LR model was biased towards underestimating the iceberg drafts. The premium LR model outperformed the previous empirical models. Ultimately, a set of LR-based relationships were derived for estimating the iceberg drafts for practical engineering applications, e.g., the early stages of the iceberg management projects.
Recent offshore oil and gas loading facilities developed in the Arctic area have led to a considerable awareness of the iceberg draft approximation, where deep keel icebergs may gouge the ocean floor, and these submarine infrastructures would be damaged in the shallower waters. Developing reliable solutions to estimate the iceberg draft requires a profound understanding of the problem’s dominant parameters. As such, the dimensionless groups of the parameters affecting the iceberg draft estimation were determined for the first time in the present study. Using the dimensionless groups recognized and the linear regression (LR) analysis, nine LR models (i.e., LR 1 to LR 9) were developed and then validated using a comprehensive dataset, which has been constructed in this study. A sensitivity analysis distinguished the premium LR models and important dimensionless groups. The best LR model, as a function of all dimensionless parameters, was able to estimate the iceberg draft with the highest level of precision and correlation along with the lowest degree of complexity. The ratio of iceberg length to iceberg height as the “iceberg length ratio” and the ratio of iceberg width to iceberg height as the “iceberg width ratio” was detected as the important dimensionless groups in the estimation of the iceberg draft. An uncertainty analysis demonstrated that the best LR model was biased towards underestimating the iceberg drafts. The premium LR model outperformed the previous empirical models. Ultimately, a set of LR-based relationships were derived for estimating the iceberg drafts for practical engineering applications, e.g., the early stages of the iceberg management projects.
2023, 37(1): 73-84.
doi: 10.1007/s13344-023-0007-5
Abstract:
The three-bucket jacket foundation is a new type of foundation for offshore wind turbine that has the advantages of fast construction speed and suitability for deep water. The study of the hoisting and launching process is of great significance to ensure construction safety in actual projects. In this paper, a new launching technology is proposed that is based on the foundation of the three-bucket jacket for offshore wind turbine. A complete time domain simulation of the launching process of three-bucket jacket foundation is carried out by a theoretical analysis combined with hydrodynamic software Moses. At the same time, the effects of different initial air storage and sea conditions on the motion response of the structure and the hoisting cable tension are studied. The results show that the motion response of the structure is the highest when it is lowered to 1.5 times the bucket height. The natural period of each degree of freedom of the structure increases with the increase of the lowering depth. The structural motion response and the hoisting cable tension vary greatly in the early phases of Stages I and III, smaller in Stage II, and gradually stabilize in the middle and late phases of Stage III.
The three-bucket jacket foundation is a new type of foundation for offshore wind turbine that has the advantages of fast construction speed and suitability for deep water. The study of the hoisting and launching process is of great significance to ensure construction safety in actual projects. In this paper, a new launching technology is proposed that is based on the foundation of the three-bucket jacket for offshore wind turbine. A complete time domain simulation of the launching process of three-bucket jacket foundation is carried out by a theoretical analysis combined with hydrodynamic software Moses. At the same time, the effects of different initial air storage and sea conditions on the motion response of the structure and the hoisting cable tension are studied. The results show that the motion response of the structure is the highest when it is lowered to 1.5 times the bucket height. The natural period of each degree of freedom of the structure increases with the increase of the lowering depth. The structural motion response and the hoisting cable tension vary greatly in the early phases of Stages I and III, smaller in Stage II, and gradually stabilize in the middle and late phases of Stage III.
2023, 37(1): 85-100.
doi: 10.1007/s13344-023-0008-4
Abstract:
Sea-crossing bridges are affected by random wind–wave–undercurrent coupling loads, due to the complex marine environment. The dynamic response of long-span Rail-cum-Road cable-stayed bridges is particularly severe under their influence, potentially leading to safety problems. In this paper, a fluid–structure separation solution method is implemented using Ansys–Midas co-simulation, in order to solve the above issues effectively while using less computational resources. The feasibility of the method is verified by comparing the tower top displacement response with relevant experimental data. From time and frequency domain perspectives, the displacement and acceleration responses of the sea-crossing Rail-cum-Road cable-stayed bridge influenced by wave-only, wind–wave, and wind–wave–undercurrent coupling are comparatively studied. The results indicate that the displacement and acceleration of the front bearing platform top are more significant than those of the rear bearing platform. The dominant frequency under wind–wave–undercurrent coupling is close to the natural vibration frequencies of several bridge modes, such that wind–wave–undercurrent coupling is more likely to cause a resonance effect in the bridge. Compared with the wave-only and wind–wave coupling, wind–wave–undercurrent coupling can excite bridges to produce larger displacement and acceleration responses: at the middle of the main girder span, compared with the wave-only case, the maximum displacement in the transverse bridge direction increases by 23.58% and 46.95% in the wind–wave and wind–wave–undercurrent coupling cases, respectively; at the tower top, the variation in the amplitude of the displacement and acceleration responses of wind–wave and wind–wave–undercurrent coupling are larger than those in the wave-only case, where the acceleration change amplitude of the tower top is from −0.93 to 0.86 m/s2 in the wave-only case, from −2.2 to 2.1 m/s2 under wind–wave coupling effect, and from −2.6 to 2.65 m/s2 under wind–wave–undercurrent coupling effect, indicating that the tower top is mainly affected by wind loads, but wave and undercurrent loads cannot be neglected.
Sea-crossing bridges are affected by random wind–wave–undercurrent coupling loads, due to the complex marine environment. The dynamic response of long-span Rail-cum-Road cable-stayed bridges is particularly severe under their influence, potentially leading to safety problems. In this paper, a fluid–structure separation solution method is implemented using Ansys–Midas co-simulation, in order to solve the above issues effectively while using less computational resources. The feasibility of the method is verified by comparing the tower top displacement response with relevant experimental data. From time and frequency domain perspectives, the displacement and acceleration responses of the sea-crossing Rail-cum-Road cable-stayed bridge influenced by wave-only, wind–wave, and wind–wave–undercurrent coupling are comparatively studied. The results indicate that the displacement and acceleration of the front bearing platform top are more significant than those of the rear bearing platform. The dominant frequency under wind–wave–undercurrent coupling is close to the natural vibration frequencies of several bridge modes, such that wind–wave–undercurrent coupling is more likely to cause a resonance effect in the bridge. Compared with the wave-only and wind–wave coupling, wind–wave–undercurrent coupling can excite bridges to produce larger displacement and acceleration responses: at the middle of the main girder span, compared with the wave-only case, the maximum displacement in the transverse bridge direction increases by 23.58% and 46.95% in the wind–wave and wind–wave–undercurrent coupling cases, respectively; at the tower top, the variation in the amplitude of the displacement and acceleration responses of wind–wave and wind–wave–undercurrent coupling are larger than those in the wave-only case, where the acceleration change amplitude of the tower top is from −0.93 to 0.86 m/s2 in the wave-only case, from −2.2 to 2.1 m/s2 under wind–wave coupling effect, and from −2.6 to 2.65 m/s2 under wind–wave–undercurrent coupling effect, indicating that the tower top is mainly affected by wind loads, but wave and undercurrent loads cannot be neglected.
2023, 37(1): 101-114.
doi: 10.1007/s13344-023-0009-3
Abstract:
Wind farms generally consist of a single turbine installed with the same hub height. As the scale of turbines increases, wake interference between turbines becomes increasingly significant, especially for floating wind turbines (FWT). Some researchers find that wind farms with multiple hub heights could increase the annual energy production (AEP), while previous studies also indicate that wake meandering could increase fatigue loading. This study investigates the wake interaction within a hybrid floating wind farm with multiple hub heights. In this study, FAST.Farm is employed to simulate a hybrid wind farm which consists of four semi-submersible FWTs (5MW and 15MW) with two different hub heights. Three typical wind speeds (below-rated, rated, and over-rated) are considered in this paper to investigate the wake meandering effects on the dynamics of two FWTs. Damage equivalent loads (DEL) of the turbine critical components are computed and analyzed for several arrangements determined by the different spacing of the four turbines. The result shows that the dynamic wake meandering significantly affects downstream turbines’ global loadings and load effects. Differences in DEL show that blade-root flapwise bending moments and mooring fairlead tensions are sensitive to the spacing of the turbines.
Wind farms generally consist of a single turbine installed with the same hub height. As the scale of turbines increases, wake interference between turbines becomes increasingly significant, especially for floating wind turbines (FWT). Some researchers find that wind farms with multiple hub heights could increase the annual energy production (AEP), while previous studies also indicate that wake meandering could increase fatigue loading. This study investigates the wake interaction within a hybrid floating wind farm with multiple hub heights. In this study, FAST.Farm is employed to simulate a hybrid wind farm which consists of four semi-submersible FWTs (5MW and 15MW) with two different hub heights. Three typical wind speeds (below-rated, rated, and over-rated) are considered in this paper to investigate the wake meandering effects on the dynamics of two FWTs. Damage equivalent loads (DEL) of the turbine critical components are computed and analyzed for several arrangements determined by the different spacing of the four turbines. The result shows that the dynamic wake meandering significantly affects downstream turbines’ global loadings and load effects. Differences in DEL show that blade-root flapwise bending moments and mooring fairlead tensions are sensitive to the spacing of the turbines.
2023, 37(1): 115-130.
doi: 10.1007/s13344-023-0010-x
Abstract:
To develop and utilize marine resources in the deep sea, the higher requirements for floating structures, which are operated in marine environment for a long term, have been put forward. Reasonable structure type and accurate force analysis are favorable guarantees to improve the survival performance and working performance of the floating structures. Floating spheres fastened by mooring cable were widely used in floating structures. In this paper, the wave forces of the floating sphere are efficiently and accurately calculated by solving the geometric relationship between the non-submerged floating sphere and wave surface. Combined with the hydrodynamic calculation of mooring cables based on the lumped mass method, the coupled motion model of multi-floating spheres fastened by multi-mooring cable was established under wave action. Furthermore, according to the floating structures fastened by mooring cable in the actual ocean engineering, the topological method of multi-mooring cables fastening the multi-floating spheres was expounded from simple to complex. Finally, the modeling method and preliminarily hydrodynamic characteristics of the fastened floating structures, including the mooring system of renewable energy devices, ocean buoy, and coral nursery, were presented and analyzed in detail. The obtained results showed that the method for calculating the wave force on the floating sphere developed in this paper can accurately describe the motion process of the floating mooring sphere and the force on the mooring cable. Also, the topological method of multiple buoys and multiple mooring cables could efficiently establish various numerical hydrodynamic models of fastened buoys in ocean engineering.
To develop and utilize marine resources in the deep sea, the higher requirements for floating structures, which are operated in marine environment for a long term, have been put forward. Reasonable structure type and accurate force analysis are favorable guarantees to improve the survival performance and working performance of the floating structures. Floating spheres fastened by mooring cable were widely used in floating structures. In this paper, the wave forces of the floating sphere are efficiently and accurately calculated by solving the geometric relationship between the non-submerged floating sphere and wave surface. Combined with the hydrodynamic calculation of mooring cables based on the lumped mass method, the coupled motion model of multi-floating spheres fastened by multi-mooring cable was established under wave action. Furthermore, according to the floating structures fastened by mooring cable in the actual ocean engineering, the topological method of multi-mooring cables fastening the multi-floating spheres was expounded from simple to complex. Finally, the modeling method and preliminarily hydrodynamic characteristics of the fastened floating structures, including the mooring system of renewable energy devices, ocean buoy, and coral nursery, were presented and analyzed in detail. The obtained results showed that the method for calculating the wave force on the floating sphere developed in this paper can accurately describe the motion process of the floating mooring sphere and the force on the mooring cable. Also, the topological method of multiple buoys and multiple mooring cables could efficiently establish various numerical hydrodynamic models of fastened buoys in ocean engineering.
2023, 37(1): 131-144.
doi: 10.1007/s13344-023-0011-9
Abstract:
Tidal bore is a special and intensive form of flow movement induced by tidal effect in estuary areas, which has complex characteristics of profile, propagation and flow velocity. Although it has been widely studied for the generation mechanism, propagation features and influencing factors, the curved channel will complicate the characteristics of tidal bore propagation, which need further investigation compared with straight channel. In this study, the flume experiments for both undular and breaking bores’ propagation in curved channel are performed to measure the free-surface elevation and flow velocity by ultrasonic sensors and ADV respectively. The propagation characteristics, including tidal bore height, cross-section surface gradient, tidal bore propagation celerity, and flow velocity are obtained for both sides of the curved channel. And three bore intensities are set for each type of tidal bores. The free-surface gradients are consistently enlarged in high-curvature section for undular and breaking bores, but have distinct behaviors in low-curvature section. The spatial distributions of tidal bore propagation celerity and flow velocity are compared between concave and convex banks. This work will provide experimental reference for engineering design of beach and seawall protection, erosion reduction and siltation promotion in estuary areas with the existence of tidal bores.
Tidal bore is a special and intensive form of flow movement induced by tidal effect in estuary areas, which has complex characteristics of profile, propagation and flow velocity. Although it has been widely studied for the generation mechanism, propagation features and influencing factors, the curved channel will complicate the characteristics of tidal bore propagation, which need further investigation compared with straight channel. In this study, the flume experiments for both undular and breaking bores’ propagation in curved channel are performed to measure the free-surface elevation and flow velocity by ultrasonic sensors and ADV respectively. The propagation characteristics, including tidal bore height, cross-section surface gradient, tidal bore propagation celerity, and flow velocity are obtained for both sides of the curved channel. And three bore intensities are set for each type of tidal bores. The free-surface gradients are consistently enlarged in high-curvature section for undular and breaking bores, but have distinct behaviors in low-curvature section. The spatial distributions of tidal bore propagation celerity and flow velocity are compared between concave and convex banks. This work will provide experimental reference for engineering design of beach and seawall protection, erosion reduction and siltation promotion in estuary areas with the existence of tidal bores.
2023, 37(1): 145-153.
doi: 10.1007/s13344-023-0012-8
Abstract:
Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography are investigated by numerical simulations based on a Mixed Euler–Lagrange (MEL) method. The transition is accomplished by the ship traveling from the depth h1 into the depth h2 via a step bottom. A small tsunami would be created after this transition. However, the unsteady wave-making resistance induced by this new phenomenon has not been well documented by literature. Therefore, the main purpose of the present study is to quantify the effects of an uneven bottom on the unsteady wash waves and wave-making resistance acting on the ship. An upwind differential scheme is commonly used in the Euler method to deal with the convection terms under free-surface condition to prevent waves in the upstream. Evidently, it cannot be applied to the present problem due to upstream waves generated by the ship would be dampened by the upwind scheme. The central differential scheme provides more accurate results, but it is not unconditionally stable. An MEL method is therefore employed to investigate the upstream wave generated by the ship moving over the uneven bottom. Simulation results show that the hydrodynamic interaction between the ship and the uneven bottom could initiate an upstream tsunami, as well as unsteady wave-making resistance on ships. The unsteady wave-making resistance oscillates periodically, and the amplitude and period of the oscillations are highly dependent on speed and water depth.
Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography are investigated by numerical simulations based on a Mixed Euler–Lagrange (MEL) method. The transition is accomplished by the ship traveling from the depth h1 into the depth h2 via a step bottom. A small tsunami would be created after this transition. However, the unsteady wave-making resistance induced by this new phenomenon has not been well documented by literature. Therefore, the main purpose of the present study is to quantify the effects of an uneven bottom on the unsteady wash waves and wave-making resistance acting on the ship. An upwind differential scheme is commonly used in the Euler method to deal with the convection terms under free-surface condition to prevent waves in the upstream. Evidently, it cannot be applied to the present problem due to upstream waves generated by the ship would be dampened by the upwind scheme. The central differential scheme provides more accurate results, but it is not unconditionally stable. An MEL method is therefore employed to investigate the upstream wave generated by the ship moving over the uneven bottom. Simulation results show that the hydrodynamic interaction between the ship and the uneven bottom could initiate an upstream tsunami, as well as unsteady wave-making resistance on ships. The unsteady wave-making resistance oscillates periodically, and the amplitude and period of the oscillations are highly dependent on speed and water depth.
2023, 37(1): 154-164.
doi: 10.1007/s13344-023-0013-7
Abstract:
Freak waves are commonly characterized by strong-nonlinearity, and the wave steepness, which is calculated from the wavelength, is a measure of the degree of the wave nonlinearity. Moreover, the wavelength can describe the locally spatial characteristics of freak waves. Generally, the wavelengths of freak waves are estimated from the dispersion relations of Stokes waves. This paper concerns whether this approach enables a consistent estimate of the wavelength of freak waves. The two- (unidirectional, long-crested) and three-dimensional (multidirectional, short-crested) freak waves are simulated experimentally through the dispersive and directional focusing of component waves, and the wavelengths obtained from the surface elevations measured by the wave gauge array are compared with the results from the linear, 3rd-order and 5th-order Stokes wave theories. The comparison results suggest that the 3rd-order theory estimates the wavelengths of freak waves with higher accuracy than the linear and 5th-order theories. Furthermore, the results allow insights into the dominant factors. It is particularly noteworthy that the accuracy is likely to depend on the wave period, and that the wavelengths of longer period freak waves are overestimated but the wavelengths are underestimated for shorter period ones. In order to decrease the deviation, a modified formulation is presented to predict the wavelengths of two- and three-dimensional freak waves more accurately than the 3rd-order dispersion relation, by regression analysis. The normalized differences between the predicted and experimental results are over 50% smaller for the modified model suggested in this study compared with the 3rd-order dispersion relation.
Freak waves are commonly characterized by strong-nonlinearity, and the wave steepness, which is calculated from the wavelength, is a measure of the degree of the wave nonlinearity. Moreover, the wavelength can describe the locally spatial characteristics of freak waves. Generally, the wavelengths of freak waves are estimated from the dispersion relations of Stokes waves. This paper concerns whether this approach enables a consistent estimate of the wavelength of freak waves. The two- (unidirectional, long-crested) and three-dimensional (multidirectional, short-crested) freak waves are simulated experimentally through the dispersive and directional focusing of component waves, and the wavelengths obtained from the surface elevations measured by the wave gauge array are compared with the results from the linear, 3rd-order and 5th-order Stokes wave theories. The comparison results suggest that the 3rd-order theory estimates the wavelengths of freak waves with higher accuracy than the linear and 5th-order theories. Furthermore, the results allow insights into the dominant factors. It is particularly noteworthy that the accuracy is likely to depend on the wave period, and that the wavelengths of longer period freak waves are overestimated but the wavelengths are underestimated for shorter period ones. In order to decrease the deviation, a modified formulation is presented to predict the wavelengths of two- and three-dimensional freak waves more accurately than the 3rd-order dispersion relation, by regression analysis. The normalized differences between the predicted and experimental results are over 50% smaller for the modified model suggested in this study compared with the 3rd-order dispersion relation.
2023, 37(1): 165-174.
doi: 10.1007/s13344-023-0014-6
Abstract:
The interface mechanical behavior of a monopile is an important component of the overall offshore wind turbine structure design. Understanding the soil−structure interaction, particularly the initial soil−structure stiffness, has a significant impact on the study of natural frequency and dynamic response of the monopile. In this paper, a simplified method for estimating the interface mechanical behavior of monopiles under initial lateral loads is proposed. Depending on the principle of minimum potential energy and virtual work theory, the functions of soil reaction components at the interface of monopiles are derived; MATLAB programming has been used to simplify the functions of the initial stiffness by fitting a large number of examples; then the functions are validated against the field test data and FDM results. This method can modify the modulus of the subgrade reaction in the p−y curve method for the monopile-supported offshore wind turbine system.
The interface mechanical behavior of a monopile is an important component of the overall offshore wind turbine structure design. Understanding the soil−structure interaction, particularly the initial soil−structure stiffness, has a significant impact on the study of natural frequency and dynamic response of the monopile. In this paper, a simplified method for estimating the interface mechanical behavior of monopiles under initial lateral loads is proposed. Depending on the principle of minimum potential energy and virtual work theory, the functions of soil reaction components at the interface of monopiles are derived; MATLAB programming has been used to simplify the functions of the initial stiffness by fitting a large number of examples; then the functions are validated against the field test data and FDM results. This method can modify the modulus of the subgrade reaction in the p−y curve method for the monopile-supported offshore wind turbine system.
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