2018 Vol.32(4)
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Experimental Investigation on the Extreme Waves Induced by Single Wave Packets in Finite Water Depth
2018, 32(4): 375-387.
doi: 10.1007/s13344-018-0040-y
Abstract:
Single Gaussian wave groups with different initial wave steepness \begin{document}$ \textit{ε}_0$\end{document} ![]()
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and width N are produced in laboratory in finite depth to study the nonlinear evolution, the extreme events and breaking. The results show that wave groups with larger \begin{document}$ \textit{ε}_0$\end{document} ![]()
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will evolve to be several envelope solitons (short wave groups). By analyzing geometric parameters, a break in the evolution of the wave elevation and asymmetric parameters after extreme wave may be an indicator for the inception of refocus and the maximal wave moving to the middle, namely, wave down-shift occurs. The analysis of the surface elevations with HHT (Hilbert-Huang Transform), which presents the concrete local variation of energy in time and frequency can be exhibited clearly, reveals that the higher frequency components play a major role in forming the extreme event and the contribution to the nonlinearity. Instantaneous energy and frequency in the vicinity of the extreme wave are also examined locally. For spilling breakers, the energy residing in the whole wave front dissipates much more due to breaking, while the energy in the rear of wave crest loses little, and the intra-wave frequency modulation increases as focus. It illustrates that the maximal first order instantaneous frequency f1 and the largest crest tend to emerge at the same time after extreme wave when significant energy dissipation happens, and vice versa. In addition, it shows that there is no obvious relation of the CDN (combined degree of nonlinearity) to the wave breaking for the single Gaussian wave group in finite water depth.
Single Gaussian wave groups with different initial wave steepness
2018, 32(4): 388-399.
doi: 10.1007/s13344-018-0041-x
Abstract:
This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics (CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom (3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step. The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes (sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.
This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics (CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom (3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step. The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes (sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.
Experimental Study on Sloshing Characteristics in the Elastic Tank Based on Morlet Wavelet Transform
2018, 32(4): 400-412.
doi: 10.1007/s13344-018-0042-9
Abstract:
Hydroelastic effect of sloshing is studied through an experimental investigation. Different excitation frequencies are considered with low-fill-depth and large amplitude. Morlet wavelet transform is introduced to analyze the free surface elevations and sloshing pressures. It focuses on variations and distributions of the wavelet energy in elastic tanks. The evolutions of theoretical and experimental wavelet spectra are discussed and the corresponding Fourier spectrums are compared. Afterwards, average values of the wavelet spectra are extracted to do a quantitative study at various points. From the wavelet analysis, sloshing energies are mainly distributed around the external excitation frequency and expanded to high frequencies under violent condition. In resonance, experimental wavelet energy of the elevation in elastic tanks is obviously less than that in the rigid one; for sloshing pressures, the elastic wavelet energy close to the rigid one and conspicuous impulse is observed. It recommends engineers to concern the primary natural frequency and impulsive peak pressures.
Hydroelastic effect of sloshing is studied through an experimental investigation. Different excitation frequencies are considered with low-fill-depth and large amplitude. Morlet wavelet transform is introduced to analyze the free surface elevations and sloshing pressures. It focuses on variations and distributions of the wavelet energy in elastic tanks. The evolutions of theoretical and experimental wavelet spectra are discussed and the corresponding Fourier spectrums are compared. Afterwards, average values of the wavelet spectra are extracted to do a quantitative study at various points. From the wavelet analysis, sloshing energies are mainly distributed around the external excitation frequency and expanded to high frequencies under violent condition. In resonance, experimental wavelet energy of the elevation in elastic tanks is obviously less than that in the rigid one; for sloshing pressures, the elastic wavelet energy close to the rigid one and conspicuous impulse is observed. It recommends engineers to concern the primary natural frequency and impulsive peak pressures.
2018, 32(4): 413-421.
doi: 10.1007/s13344-018-0043-8
Abstract:
A series of experimental tests of passive VIV suppression of an inclined flexible cylinder with round-sectioned helical strakes were carried out in a towing tank. During the tests, the cylinder models fitted with and without helical strakes were towed along the tank. The towing velocity ranged from 0.05 to 1.0 m/s with an interval of 0.05 m/s. Four different yaw angles (a=0°, 15°, 30° and 45°), defined as the angle between the axis of the cylinder and the plane orthogonal of the oncoming flow, were selected in the experiment. The main purpose of present experimental work is to further investigate the VIV suppression effectiveness of round-sectioned helical strakes on the inclined flexible cylinder. The VIV responses of the smooth cylinder and the cylinder with square-sectioned strakes under the same experimental condition were also presented for comparison. The experimental results indicated that the round-sectioned strake basically had a similar effect on VIV suppression compared with the square-sectioned one, and both can significantly reduce the VIV of the vertical cylinder which corresponded to the case of a=0°. But with the increase of yaw angle, the VIV suppression effectiveness of both round- and square-section strakes deteriorated dramatically, the staked cylinder even had a much stronger vibration than the smooth one did in the in-line (IL) direction.
A series of experimental tests of passive VIV suppression of an inclined flexible cylinder with round-sectioned helical strakes were carried out in a towing tank. During the tests, the cylinder models fitted with and without helical strakes were towed along the tank. The towing velocity ranged from 0.05 to 1.0 m/s with an interval of 0.05 m/s. Four different yaw angles (a=0°, 15°, 30° and 45°), defined as the angle between the axis of the cylinder and the plane orthogonal of the oncoming flow, were selected in the experiment. The main purpose of present experimental work is to further investigate the VIV suppression effectiveness of round-sectioned helical strakes on the inclined flexible cylinder. The VIV responses of the smooth cylinder and the cylinder with square-sectioned strakes under the same experimental condition were also presented for comparison. The experimental results indicated that the round-sectioned strake basically had a similar effect on VIV suppression compared with the square-sectioned one, and both can significantly reduce the VIV of the vertical cylinder which corresponded to the case of a=0°. But with the increase of yaw angle, the VIV suppression effectiveness of both round- and square-section strakes deteriorated dramatically, the staked cylinder even had a much stronger vibration than the smooth one did in the in-line (IL) direction.
2018, 32(4): 422-430.
doi: 10.1007/s13344-018-0044-7
Abstract:
Logistical supply is costly for the deepwater oil and gas exploitation, thereby it is necessary to develop a novel power supply solution to improve the offshore structure’s self-holding capacity. The two-body point absorbers, as a renewable energy device, have achieved a rapid development. Heave plate is used to constrain the truss’s motion in the two-body point absorber, and the floater moves along the truss up and down. This two-body point absorber can be considered to be an essentially mass-spring-damper system. And it is well known that the heave plates have been widely used in the Spar platform to suppress the heave motions. So if the two-body point absorber can be modified to combine with offshore floating structures, this system can not only offer electric power to support operations or daily lives for the platform, but also control the large motions in the vertical plane. Following this concept, a novel tuned heave plate (THP) system is proposed for the conventional semi-submersible platform. In order to investigate the dynamic performances of the single THP, two experiments are conducted in this paper. First, the hydrodynamic coefficients of the heave plates are studied, and then the THP experiments are carried out to analyze its dynamic performance. It can be concluded that this THP is feasible and achieves the design objective.
Logistical supply is costly for the deepwater oil and gas exploitation, thereby it is necessary to develop a novel power supply solution to improve the offshore structure’s self-holding capacity. The two-body point absorbers, as a renewable energy device, have achieved a rapid development. Heave plate is used to constrain the truss’s motion in the two-body point absorber, and the floater moves along the truss up and down. This two-body point absorber can be considered to be an essentially mass-spring-damper system. And it is well known that the heave plates have been widely used in the Spar platform to suppress the heave motions. So if the two-body point absorber can be modified to combine with offshore floating structures, this system can not only offer electric power to support operations or daily lives for the platform, but also control the large motions in the vertical plane. Following this concept, a novel tuned heave plate (THP) system is proposed for the conventional semi-submersible platform. In order to investigate the dynamic performances of the single THP, two experiments are conducted in this paper. First, the hydrodynamic coefficients of the heave plates are studied, and then the THP experiments are carried out to analyze its dynamic performance. It can be concluded that this THP is feasible and achieves the design objective.
2018, 32(4): 431-442.
doi: 10.1007/s13344-018-0045-6
Abstract:
Parametric rolling is one of five types of the ship stability failure modes as proposed by IMO. The periodic change of the metacentric height is often considered as the internal cause of this phenomenon. Parametric rolling is a complex nonlinear hydrodynamic problem, often accompanied by large amplitude vertical motions of ships. In recent years, the Reynolds-averaged Navier–Stokes (RANS) equation simulations for viscous flows have made great progress in the field of ship seakeeping. In this paper, the parametric rolling for the C11 containership in regular waves is studied both experimentally and numerically. In the experiments, parametric rolling amplitudes at different drafts, forward speeds and wave steepnesses are analyzed. The differences in the steady amplitudes of parametric rolling are observed for two drafts. The effect of the incident wave steepness (or wave amplitude) is also studied, and this supports previous results obtained on limits of the stability for parametric rolling. In numerical simulations, the ship motions of parametric rolling are analyzed by use of the potential-flow and viscous-flow methods. In the viscous-flow method, the Reynolds-averaged Navier–Stokes equations are solved using the overset grid method. The numerical accuracies of the two methods at different wave steepnesses are also discussed.
Parametric rolling is one of five types of the ship stability failure modes as proposed by IMO. The periodic change of the metacentric height is often considered as the internal cause of this phenomenon. Parametric rolling is a complex nonlinear hydrodynamic problem, often accompanied by large amplitude vertical motions of ships. In recent years, the Reynolds-averaged Navier–Stokes (RANS) equation simulations for viscous flows have made great progress in the field of ship seakeeping. In this paper, the parametric rolling for the C11 containership in regular waves is studied both experimentally and numerically. In the experiments, parametric rolling amplitudes at different drafts, forward speeds and wave steepnesses are analyzed. The differences in the steady amplitudes of parametric rolling are observed for two drafts. The effect of the incident wave steepness (or wave amplitude) is also studied, and this supports previous results obtained on limits of the stability for parametric rolling. In numerical simulations, the ship motions of parametric rolling are analyzed by use of the potential-flow and viscous-flow methods. In the viscous-flow method, the Reynolds-averaged Navier–Stokes equations are solved using the overset grid method. The numerical accuracies of the two methods at different wave steepnesses are also discussed.
2018, 32(4): 443-452.
doi: 10.1007/s13344-018-0046-5
Abstract:
The fluid viscosity is known to have a significant effect on the hydrodynamic characteristics which are linked to the power conversion ability of the wave energy converter (WEC). To overcome the disadvantages of case-by-case study through the experiments and numerical computations employed by the former researches, the viscous effect is studied comprehensively for multiple geometries in the present paper. The viscous effect is expressed as the viscous added mass and damping solved by the free-decay method. The computational fluid dynamics (CFD) method is employed for the calculation of the motion and flow field around the floater. The diameter to draft ratio and bottom shape are considered for the geometrical evaluation on the viscous effect. The results show that a slenderer floater presents a stronger viscous effect. Through the comparisons of the floaters with four different bottom shapes, the conical bottom is recommended in terms of low viscous effect and simple geometry for manufacture. A viscous correction formula for a series of cylindrical floaters is put forward, for the first time, to help the engineering design of outer-floaters of point-absorber WECs.
The fluid viscosity is known to have a significant effect on the hydrodynamic characteristics which are linked to the power conversion ability of the wave energy converter (WEC). To overcome the disadvantages of case-by-case study through the experiments and numerical computations employed by the former researches, the viscous effect is studied comprehensively for multiple geometries in the present paper. The viscous effect is expressed as the viscous added mass and damping solved by the free-decay method. The computational fluid dynamics (CFD) method is employed for the calculation of the motion and flow field around the floater. The diameter to draft ratio and bottom shape are considered for the geometrical evaluation on the viscous effect. The results show that a slenderer floater presents a stronger viscous effect. Through the comparisons of the floaters with four different bottom shapes, the conical bottom is recommended in terms of low viscous effect and simple geometry for manufacture. A viscous correction formula for a series of cylindrical floaters is put forward, for the first time, to help the engineering design of outer-floaters of point-absorber WECs.
2018, 32(4): 453-460.
doi: 10.1007/s13344-018-0047-4
Abstract:
Ocean wave energy converters (WECs) are obtaining more and more attentions in the world. So far, many types of converters have been invented. Oscillating body systems are a major class of WECs, which typically have one degree of freedom (DOF), and the power absorption efficiency is not quite satisfactory. In this paper, a 3-DOF WEC is proposed and a simplified frequency-domain dynamic model of the WEC depending on the linear potential theory is conducted. The performances of three geometries of the oscillating body including the cone, the cylinder and the hemisphere have been compared, and the results show that the hemisphere is more suitable for the 3-DOF WEC. Subsequently, the relationship among the parameters of the hemisphere is established based on the equal natural frequencies of the heave and pitch (or roll) motions, and the results show that lowering the center of gravity leads to the better power absorption in the pitch (or roll) motion. In the end, the power matrixes of different sizes of the hemispheres under different irregular waves are obtained, which can give a size design reference for engineers.
Ocean wave energy converters (WECs) are obtaining more and more attentions in the world. So far, many types of converters have been invented. Oscillating body systems are a major class of WECs, which typically have one degree of freedom (DOF), and the power absorption efficiency is not quite satisfactory. In this paper, a 3-DOF WEC is proposed and a simplified frequency-domain dynamic model of the WEC depending on the linear potential theory is conducted. The performances of three geometries of the oscillating body including the cone, the cylinder and the hemisphere have been compared, and the results show that the hemisphere is more suitable for the 3-DOF WEC. Subsequently, the relationship among the parameters of the hemisphere is established based on the equal natural frequencies of the heave and pitch (or roll) motions, and the results show that lowering the center of gravity leads to the better power absorption in the pitch (or roll) motion. In the end, the power matrixes of different sizes of the hemispheres under different irregular waves are obtained, which can give a size design reference for engineers.
2018, 32(4): 461-466.
doi: 10.1007/s13344-018-0048-3
Abstract:
The modified suction caisson (MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wind turbine foundation subjected to larger lateral loads compared with the imposed vertical loads. Determination of the lateral bearing capacity is a key issue for the MSC design. The formula estimating the lateral bearing capacity of the MSC was proposed in terms of the limit equilibrium method and was verified by the test results. Parametric studies on the lateral bearing capacity were also carried out. It was found that the lateral bearing capacity of the MSC increases with the increasing length and radius of the external skirt, and the lateral bearing capacity increases linearly with the increasing coefficient of subgrade reaction. The maximum lateral bearing capacity of the MSC is attained when the ratio of the radii of the internal compartment to the external skirt equals 0.82 and the ratio of the lengths of the external skirt to the internal compartment equals 0.48, provided that the steel usage of the MSC is kept constant.
The modified suction caisson (MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wind turbine foundation subjected to larger lateral loads compared with the imposed vertical loads. Determination of the lateral bearing capacity is a key issue for the MSC design. The formula estimating the lateral bearing capacity of the MSC was proposed in terms of the limit equilibrium method and was verified by the test results. Parametric studies on the lateral bearing capacity were also carried out. It was found that the lateral bearing capacity of the MSC increases with the increasing length and radius of the external skirt, and the lateral bearing capacity increases linearly with the increasing coefficient of subgrade reaction. The maximum lateral bearing capacity of the MSC is attained when the ratio of the radii of the internal compartment to the external skirt equals 0.82 and the ratio of the lengths of the external skirt to the internal compartment equals 0.48, provided that the steel usage of the MSC is kept constant.
2018, 32(4): 467-475.
doi: 10.1007/s13344-018-0049-2
Abstract:
In this paper the steady lateral growth of three-dimensional turbulent inclined turbidity current is investigated. To simulate the current, an experimental setup is developed to analyze the turbidity current for different regimes in the particle laden density currents environment. The Buckingham’s π theorem together with a dimensional analysis is implemented to derive the appropriate non-dimensional variables. The experimental results were normalized and plotted in the form of non-dimensional graphs from which a theoretical model is developed and analyzed. Based on the results obtained for the steady lateral growth, three different regimes, namely, inertia-viscous one as the first regime, buoyancy-viscous and gravity-viscous as the second and third regimes are distinguished within the current. In these regimes, the force balance is between the driving and resisting forces. Namely, in the first regime, the force balance is between the inertia and viscous forces, in the second regime, the buoyancy and viscous forces, and in the third regime, gravity and viscous forces are balanced. The experimental results indicate that the lateral growth rate in the first regime is smaller than that in the second and third regimes due to the magnitude and type of the forces involved in those regimes. According to the graphical results, the three different lateral growth rates appear when the normalized current length is smaller than about 3, between about 3 and 10, and larger than about 10. In those regions, the slopes of the data are different with respect to one another.
In this paper the steady lateral growth of three-dimensional turbulent inclined turbidity current is investigated. To simulate the current, an experimental setup is developed to analyze the turbidity current for different regimes in the particle laden density currents environment. The Buckingham’s π theorem together with a dimensional analysis is implemented to derive the appropriate non-dimensional variables. The experimental results were normalized and plotted in the form of non-dimensional graphs from which a theoretical model is developed and analyzed. Based on the results obtained for the steady lateral growth, three different regimes, namely, inertia-viscous one as the first regime, buoyancy-viscous and gravity-viscous as the second and third regimes are distinguished within the current. In these regimes, the force balance is between the driving and resisting forces. Namely, in the first regime, the force balance is between the inertia and viscous forces, in the second regime, the buoyancy and viscous forces, and in the third regime, gravity and viscous forces are balanced. The experimental results indicate that the lateral growth rate in the first regime is smaller than that in the second and third regimes due to the magnitude and type of the forces involved in those regimes. According to the graphical results, the three different lateral growth rates appear when the normalized current length is smaller than about 3, between about 3 and 10, and larger than about 10. In those regions, the slopes of the data are different with respect to one another.
2018, 32(4): 476-481.
doi: 10.1007/s13344-018-0050-9
Abstract:
Jack-up platforms of the Ocean engineering structures always withstand the vertical gravity loads which are applied to the seabed by spudcan, so it is important to determine the bearing capacity and the penetration depth of the spudcan for its geometry. In fact, it is up to the deformation law and the failure modes of soil surrounding the spudcan which can calculate the ultimate bearing capacity of the spudcan foundation on the soil seabed. By using the finite element analysis software Abaqus, the deformation law of soil around the spudcan is analyzed in detail, and the failure modes of soil surrounding the spudcan foundation are achieved. At the same time, based on the limit equilibrium theory, by use of static permissible slip-line field, the ultimate bearing capacity of the spudcan foundation is analyzed and the lower limit solution is derived theoretically, and the effect of the spudcan angle on the ultimate bearing capacity is investigated. The numerical results are compared with those obtained by the theoretical formulas deduced in this paper. On the basis of the lower limit solutions in this paper, the effect of the spudcan angle on the ultimate bearing capacity is revealed, and a practical bearing capacity formula is given to take the effect of the spudcan angle into consideration.
Jack-up platforms of the Ocean engineering structures always withstand the vertical gravity loads which are applied to the seabed by spudcan, so it is important to determine the bearing capacity and the penetration depth of the spudcan for its geometry. In fact, it is up to the deformation law and the failure modes of soil surrounding the spudcan which can calculate the ultimate bearing capacity of the spudcan foundation on the soil seabed. By using the finite element analysis software Abaqus, the deformation law of soil around the spudcan is analyzed in detail, and the failure modes of soil surrounding the spudcan foundation are achieved. At the same time, based on the limit equilibrium theory, by use of static permissible slip-line field, the ultimate bearing capacity of the spudcan foundation is analyzed and the lower limit solution is derived theoretically, and the effect of the spudcan angle on the ultimate bearing capacity is investigated. The numerical results are compared with those obtained by the theoretical formulas deduced in this paper. On the basis of the lower limit solutions in this paper, the effect of the spudcan angle on the ultimate bearing capacity is revealed, and a practical bearing capacity formula is given to take the effect of the spudcan angle into consideration.
2018, 32(4): 482-489.
doi: 10.1007/s13344-018-0051-8
Abstract:
The innovative Subsurface Tension Leg Platform (STLP), which is designed to be located below Mean Water Level (M.W.L) to minimize direct wave loading and mitigate the effect of strong surface currents, is considered as a competitive alternative system to support shallow-water rated well completion equipment and rigid risers for large ultra-deep water oil field development. A detailed description of the design philosophy of STLP has been published in the series of papers and patents. Nonetheless, design uncertainties arise as limited understanding of various parameters effects on the structural response of STLP, pertaining to the environmental loading, structural properties and hydrodynamic characteristics. This paper focuses on providing quantitative methodology on how each parameter affects the structural response of STLP, which will facilitate establishing the unique design criteria as regards to STLP. Firstly, the entire list of dimensionless groups of input and output parameters is proposed based on Vaschy-Buckingham theory. Then, numerical models are built and a series of numerical tests are carried out for validating the obtained dimensionless groups. On this basis, the calculation results of a great quantity of parametric studies on the structural response of STLP are presented and discussed in detail. Further, empirical formulae for predicting STLP response are derived through nonlinear regression analysis. Finally, conclusions and discussions are made. It has been demonstrated that the study provides a methodology for better control of key parameters and lays the foundation for optimal design of STLP. The obtained conclusions also have wide ranging applicability in reference to the engineering design and design analysis aspects of deepwater buoy supporting installations, such as Grouped SLOR or TLR system.
The innovative Subsurface Tension Leg Platform (STLP), which is designed to be located below Mean Water Level (M.W.L) to minimize direct wave loading and mitigate the effect of strong surface currents, is considered as a competitive alternative system to support shallow-water rated well completion equipment and rigid risers for large ultra-deep water oil field development. A detailed description of the design philosophy of STLP has been published in the series of papers and patents. Nonetheless, design uncertainties arise as limited understanding of various parameters effects on the structural response of STLP, pertaining to the environmental loading, structural properties and hydrodynamic characteristics. This paper focuses on providing quantitative methodology on how each parameter affects the structural response of STLP, which will facilitate establishing the unique design criteria as regards to STLP. Firstly, the entire list of dimensionless groups of input and output parameters is proposed based on Vaschy-Buckingham theory. Then, numerical models are built and a series of numerical tests are carried out for validating the obtained dimensionless groups. On this basis, the calculation results of a great quantity of parametric studies on the structural response of STLP are presented and discussed in detail. Further, empirical formulae for predicting STLP response are derived through nonlinear regression analysis. Finally, conclusions and discussions are made. It has been demonstrated that the study provides a methodology for better control of key parameters and lays the foundation for optimal design of STLP. The obtained conclusions also have wide ranging applicability in reference to the engineering design and design analysis aspects of deepwater buoy supporting installations, such as Grouped SLOR or TLR system.
2018, 32(4): 490-500.
doi: 10.1007/s13344-018-0052-7
Abstract:
In order to solve unsteady incompressible Navier–Stokes (N–S) equations, a new stabilized finite element method, called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation. After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.
In order to solve unsteady incompressible Navier–Stokes (N–S) equations, a new stabilized finite element method, called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation. After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.
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