A numerical simulation and an experimental study on vortex-induced motion（VIM） of a new type of deep draft multi-columns floating drilling production, storage and offloading（FDPSO） are presented in this paper. The...A numerical simulation and an experimental study on vortex-induced motion（VIM） of a new type of deep draft multi-columns floating drilling production, storage and offloading（FDPSO） are presented in this paper. The main dimension, the special variable cross-section column and the cabin arrangement of the octagonal pontoon are introduced based on the result. The numerical simulation is adapted to study the effects of current incidence angles and reduced velocities on this platform’s sway motion response. The 300 m water depth equivalent truncated mooring system is adopted for the model tests. The model tests are carried out to check the reliability of numerical simulation. The results consist of surge, sway and yaw motions, as well as motion trajectories. The maximum sway amplitudes for different types of offshore platform is also studied. The main results show that the peak frequencies of sway motion under different current incidence angles and reduced velocities vary around the natural frequency. The analysis result of flow field indicates that the change of distribution of vortex in vertical presents significant influences on the VIM of platform. The trend of sway amplitude ratio curve of this new type FDPSO differs from the other types of platform. Under 45° current incidence angle, the sway amplitude of this new type of FDPSO is much smaller than those of other types of offshore platform at 4.4 ≤ V;≤ 8.9. The typical ‘8’ shape trajectory does not appear in the platform’s motion trajectories.展开更多
Spar platforms could be subject to vortex-induced-motions(VIM) in certain current conditions.Lockin is a phenomenon which occurs in a range of reduced velocities in VIM.In this paper,a new concept of spar platform cal...Spar platforms could be subject to vortex-induced-motions(VIM) in certain current conditions.Lockin is a phenomenon which occurs in a range of reduced velocities in VIM.In this paper,a new concept of spar platform called cell-truss spar is studied using both computational fluid dynamics(CFD) and model test to investigate the VIM of the spar under different reduced velocities.The unique configuration of the cell-truss spar is carefully considered,and the unsteady flow around the spar is calculated and visualized in CFD simulations.A physical model with a scale ratio of 1:100 of the cell-truss spar is fabricated,and model tests are carried out in the current-generating ocean engineering basin.Many important parameters in VIM of the cell-truss spar are obtained,the occurrence of lock-in phenomenon is successfully simulated,and the mechanism and rules of lock-in are analyzed.展开更多
This paper presents 3D （three-dimensional） CFD （computational fluid dynamic） simulation to analyse the FIR （flow-induced response） especially the yaw motion of a buoyancy can. The numerical cases are conducted w...This paper presents 3D （three-dimensional） CFD （computational fluid dynamic） simulation to analyse the FIR （flow-induced response） especially the yaw motion of a buoyancy can. The numerical cases are conducted with a buoyancy can under different reduced velocities utilizing our in-house code naoe-FOAM-SJTU, a solver based on the open source toolkit OpenFOAM. SST-DDES （shear-stress transport-delayed detached-eddy simulation） model is applied to handle the flowseparation and overset grid method is utilized to solve a large amplitude 6-DOF （6 degrees of freedom） motions. Free decay test and VIM （vortex-induced motion） test are built numerically. In VIM cases, the responses of trajectory, amplitude, frequency are calculated in a series of reduced velocities. With the increase of reduced velocity, yaw frequency is increased, which is similar to surge and sway frequency. And yaw frequency is equal to the sway frequency, which is consistent with experimental results. Furthermore, comparing two cases, one fixed in rotation and the other one free in rotation, it can be concluded that release in the degree of rotation can decrease the sway amplitude but make no difference in the surge amplitude.展开更多
A Deep Draft Semi-submersible （DDS） under certain flow conditions could be subjected to Vortex-Induced Motions （VIM）, which significantly influences the loads on and life fatigue of the moorings and the risers. To...A Deep Draft Semi-submersible （DDS） under certain flow conditions could be subjected to Vortex-Induced Motions （VIM）, which significantly influences the loads on and life fatigue of the moorings and the risers. To investigate the VIM of a DDS with four rectangular section columns in waves coupled with a uniform current, a numerical study using the computational fluid dynamics （CFD） method was conducted. The issues of the VIM of multi-column floaters can be con＇,＇eniently converted to the issues of oscillating cylinders in fluid cross flows. This paper looks into the CFD numerical simulation of infinite cylinders having rectangular sections in a two-dimensional sinusoidal time- dependent flow field coupled with a uniform current. The resulted hydrodynamic forces and motion responses in different oscillatory flows plus currents both aligned in the same direction for the incidence of 135° of the DDS relative to the flow are compared with the ones in current only cases. The results show that the VIM response of this geometric arrangement of a DDS with four rectangular columns in a current combined with oscillatory flows is more evident than that in the current only case. The oscillatory flows and waves have the significant influence on the VIM response, forces and trajectory, in-plane motions of the DDS.展开更多
A phenomenological model for predicting the vortex-induced motion (VIM) of a single-column platform with non- linear stiffness has been proposed. The VIM model is based on the couple of the Duffing-van der Pol oscilla...A phenomenological model for predicting the vortex-induced motion (VIM) of a single-column platform with non- linear stiffness has been proposed. The VIM model is based on the couple of the Duffing-van der Pol oscillators and the motion equations with non-linear terms. The model with liner stiffness is presented for comparison and their results are compared with the experiments in order to calibrate the model. The computed results show that the predicted VIM amplitudes and periods of oscillation are in qualitative agreements with the experimental data. Compared with the results with linear stiffness, it is found that the application of non-linear stiffness causes the significant reductions in the in-line and transverse motion amplitudes. Under the non-linear stiffness constraint, the lock-in behavior is still identified at 8<Ur<15, and the trajectories of the VIM on the xy plane with eight-figure patterns are maintained. The results with different non-linear geometrically parameters show that both in-line and transverse non-linear characteristics can significantly affect the predict in-line and transverse motion amplitudes. Furthermore, the computed results for different aspect ratios indicate that the in-line and transverse motion amplitudes increase with the growth of aspect ratio, and the range of lock-in region is enlarged for the large aspect ratio.展开更多
A numerical simulation analysis is conducted to examine the unsteady hydrodynamic characteristics of vortex-induced vibration(VIV)and the suppression effect of helical strakes on VIV in subsea pipelines.The analysis u...A numerical simulation analysis is conducted to examine the unsteady hydrodynamic characteristics of vortex-induced vibration(VIV)and the suppression effect of helical strakes on VIV in subsea pipelines.The analysis uses the standard k−εturbulence model for 4.5-and 12.75-inch pipes,and its accuracy is verified by comparing the results with large-scale hydrodynamic experiments.These experiments are designed to evaluate the suppression efficiency of VIV with and without helical strakes,focusing on displacement and drag coefficients under different flow conditions.Furthermore,the influence of important geometric parameters of the helical strakes on drag coefficients and VIV suppression efficiency at different flow rates is compared and discussed.Numerical results agree well with experimental data for drag coefficient and vortex shedding frequency.Spring-pipe self-excited vibration experimental tests reveal that the installation of helical strakes substantially reduces the drag coefficient of VIV within a certain flow rate range,achieving suppression efficiencies exceeding 90%with strake heights larger than 0.15D.Notably,the optimized parameter combination of helical strakes,with a pitch of 15D,a fin height of 0.2D,and 45°edge slopes,maintains high suppression efficiency,thereby exhibiting superior performance.This study provides a valuable reference for the design and application of helical strakes and VIV suppression in subsea engineering.展开更多
A deep-sea mining riser is a crucial component of the system used to lift seafloor mineral resources to the vessel.It is prone to damage and failure because of harsh environmental conditions and internal fluid erosion...A deep-sea mining riser is a crucial component of the system used to lift seafloor mineral resources to the vessel.It is prone to damage and failure because of harsh environmental conditions and internal fluid erosion.Furthermore,damage can impact the response characteristics of the riser,but varying environmental loadings easily mask it.Thus,distin-guishing between riser damage and environmental effects poses a considerable challenge.To address this issue,a cantilevered model is created for a deep-sea mining riser via the concentrated mass method,and a time-domain analytical strategy is developed.The vortex-induced vibration(VIV)response characteristics of the riser are initially examined,considering various damage conditions and flow velocities.The study results revealed four primary observations:(a)effective tension can serve as a reliable indicator for identifying damage at lower velocities;(b)there are noticeable differences in displacement between the healthy and damaged risers in the in-line direction rather than the cross-flow direction;(c)frequency characteristics can more effectively distinguish the damage conditions at high flow velocities,with the mean square frequency and frequency variance being more effective than the centroid frequency and root variance frequency;(d)displacement differences are more sensitive to damage occurring near the top and bottom of the riser,while both velocity variations and structural damage can influence displacements,especially in regions between modal nodes.The vibrational behavior and damage indicators are clarified for structural health monitoring of deep-sea mining risers during lifting operations.展开更多
The position deviation of the underwater manipulator generated by vortex-induced vibration(VIV)in the shear flow increases relative to that in the uniform flow.Thus,this study established an experimental platform to i...The position deviation of the underwater manipulator generated by vortex-induced vibration(VIV)in the shear flow increases relative to that in the uniform flow.Thus,this study established an experimental platform to investigate the vibration characteristics of the underwater manipulator under shear flow.The vibration response along the manipulator was obtained and compared with that in the uniform flow.Results indicated that the velocity,test height,and flow field were the main factors affecting the VIV of the underwater manipulator.With the increase in the reduced velocity(U_(r)),the dimensionless amplitudes increased rapidly in the in-line(IL)direction with a maximum of 0.13D.The vibration responses in the cross-flow(CF)and IL directions were concentrated at positions 2,3 and positions 1,2,with peak values of 0.46 and 0.54 mm under U_(r)=1.54,respectively.In addition,the vibration frequency increased with the reduction of velocity.The dimensionless dominant frequency in the CF and IL directions varied from 0.39-0.80 and 0.35-0.64,respectively.Moreover,the ratio of the CF and IL directions was close to 1 at a lower U_(r).The standard deviation of displacement initially increased and then decreased as the height of the test location increased.The single peak value of the standard deviation showed that VIV presented a single mode.Compared with the uniform flow,the maximum and average values of VIV displacement increased by 104%and 110%under the shear flow,respectively.展开更多
Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce f...Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce fatigue failure and even cause unpredictable drilling accidents.Therefore,it is important to study the ViV characteristics of deepwater drilling riser and reveal the main controlling factors for ensuring the safe and efficient operation of deepwater drilling engineering.In this paper,the ViV of deepwater drilling riser is numerically simulated in time domain based on the discrete vortex method(DvM).A hydrodynamic analysis model and governing equation of VIV is proposed with considering the effect of riser motion using DVM and slice method,where the governing equation is solved by Runge-Kutta method.Model validation is performed,which verified the correctness and accuracy of the mechanical model and the solution method.On this basis,the influence of the number of control points,current velocity,riser outer diameter,shear flow and top tension on the ViV characteristics of deepwater drilling risers are discussed in detail.The results show that with the increase of current velocity,the vibration amplitude of deepwater drilling riser decreases obviously,while the vibration frequency increases gradually.However,if the outer diameter of riser increases,the vibration amplitude increases,while the vibration frequency decreases gradually.The top tension also has great influence on the VIV of riser.When the top tension is 1.25 G,the VIV is suppressed to a certain extent.This study has guiding significance for optimal design and engineering control of deepwater drilling riser.展开更多
Installing the splitter plates is a passive aerodynamic solution for eliminating vortex-induced vibration (VIV). However, the influences of splitter plates on the VIV and aerostatic performances are more complicated d...Installing the splitter plates is a passive aerodynamic solution for eliminating vortex-induced vibration (VIV). However, the influences of splitter plates on the VIV and aerostatic performances are more complicated due to aerodynamic interference between highway and railway decks. To study the effects of splitter plates, wind tunnel experiments for measuring VIV and aerostatic forces of twin decks under two opposite flow directions were conducted, while the surrounding flow and wind pressure of static twin decks with and without splitter plates are numerically simulated. The results showed that the incoming flow direction affects the VIV response and aerostatic coefficients. The highway deck has poor vertical and torsional VIV, and the VIV region and amplitude are different under different directions. While the railway deck only has vertical VIV when located upstream. The splitter plates can impede the process of vortex generation, shedding and impinging at the gap between twin deck, and significantly reducing the surface fluctuating pressure coefficient, thus effectively suppressing the VIV of twin decks. While, the splitter plates hurt the upstream deck regarding static wind stability and have little effect on the downstream deck. The splitter plates of appropriate width are recommended to improve VIV performances in twin parallel bridges.展开更多
Vortex-induced vibration of hydrofoils is concerned with structural safety and noise level in hydraulic machinery and marine engineering.The research on vibration characteristics under different operating conditions i...Vortex-induced vibration of hydrofoils is concerned with structural safety and noise level in hydraulic machinery and marine engineering.The research on vibration characteristics under different operating conditions is significant.In this study,numerical simulations are conducted to investigate the vortex-induced vibration responses of an elastically suspended hydrofoil with blunt trailing edge in pitch direction.The work studies the effects of four parameters,namely the structural natural frequency,mass ratio,initial attack angle,and Reynolds number on vibration characteristics,with special emphasis on frequency lock-in.Results indicate that as the structural natural frequency changes,the vibration amplitude may increase substantially within a certain frequency range,in which the vortex shedding frequency locks into the structural natural frequency,and frequency lock-in occurs.In addition,with increasing the mass ratio,the frequency range of lock-in becomes narrower,and both the upper and lower thresholds decrease.As the initial attack angle increases from 0◦to 6◦,the lock-in range gets reduced.Over the three Reynolds numbers(6×10^(5),9×10^(5),and 12×10^(5)),the lock-in range remains virtually unchanged.Moreover,for a certain structural natural frequency,modifying the mass ratio,initial attack angle,and Reynolds number could effectively suppress the vibration amplitude.展开更多
Vortex-induced vibration(VIV)of cylindrical structures is a critical fluid-structure interaction(FSI)phenomenon in ocean engineering.Simulating VIV accurately can be computationally expensive.This study presents a gra...Vortex-induced vibration(VIV)of cylindrical structures is a critical fluid-structure interaction(FSI)phenomenon in ocean engineering.Simulating VIV accurately can be computationally expensive.This study presents a graphics processing unit(GPU)-accelerated simulation model for VIV utilizing the immersed boundary lattice Boltzmann method(IB-LBM),aiming to reduce computational costs while preserving accuracy.The program is developed using machine learning library JAX,which enables parallelism on GPU and multi-GPU platforms.The model incorporates multi-GPU parallelization and multi-block grid refinement strategies to enhance computational efficiency.Validation against existing high-fidelity simulation data demonstrates good agreement.Performance tests show significant speed-ups with GPU acceleration compared to traditional CPU-based approaches.These results underscore the potential of the developed simulator as an efficient and reliable tool for in-depth parametric studies and practical engineering analysis of VIV,facilitating more rapid design iterations and risk assessments for offshore structures.展开更多
When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fa...When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.展开更多
Biomimetic design has recently received widespread attention.Inspired by the Terebridae structure,this paper provides a structural form for suppressing vortex-induced vibration(VIV)response.Four different structural f...Biomimetic design has recently received widespread attention.Inspired by the Terebridae structure,this paper provides a structural form for suppressing vortex-induced vibration(VIV)response.Four different structural forms are shown,including the traditional smooth cylinder(P0),and the Terebridae-inspired cylinder with the helical angle of 30°(P_(30)),60°(P_(60)),and 90°(P_(90)).Computational fluid dynamics(CFD)method is adopted to solve the flow pass the Terebridae-inspired structures,and the vibration equation is solved using the Newmark-βmethod.The results show that for P_(30),P_(60) and P_(90),the VIV responses are effectively suppressed in the lock-in region,and P_(60) showed the best VIV suppression performance.The transverse amplitude and the downstream amplitude can be reduced by 82.67%and 91.43%respectively for P_(60) compared with that for P0,and the peak of the mean-drag coefficient is suppressed by 53.33%.The Q-criterion vortices of P_(30),P_(60),and P_(90) are destroyed,with irregular vortices shedding.It is also found that the boundary layer separation is located on the Terebridae-inspired ribs.The twisted ribs cause the separation point to constantly change along the spanwise direction,resulting in the development of the boundary layer separation being completely destroyed.The strength of the wake flow is significantly weakened for the Terebridae-inspired cylinder.展开更多
A vortex-induced vibration(VIV)experiment of rough risers with coupling interference effect under a side-by-side arrangement was carried out in a wave-current combined flume.The roughness of the riser was characterize...A vortex-induced vibration(VIV)experiment of rough risers with coupling interference effect under a side-by-side arrangement was carried out in a wave-current combined flume.The roughness of the riser was characterized by arranging different specifications of surface attachments on the surface of the riser.Rough risers with three different roughnesses were arranged side by side with smooth risers to explore the VIV response of the riser under the combined action of roughness and interference effect,and to reveal the coupling mechanism between roughness and interference effect.The experimental results show that,compared with that of a smooth riser,the VIV of a rough riser under the coupling interference effect has a wider"lock-in"region,and the displacement decreases more significantly at a high reduced velocity,which is more likely to excite higher-order modes and frequency responses.In addition,the displacement response and frequency response of the smooth riser are not significantly affected by wake interference from the rough riser,which is caused by the decrease of the wake region due to the delay of the boundary layer separation point of the rough riser.展开更多
In order to study the response law of vortex-induced vibration(VIV)of marine risers under the combined action of roughness and interference effects,and to reveal the coupling mechanism of roughness and interference ef...In order to study the response law of vortex-induced vibration(VIV)of marine risers under the combined action of roughness and interference effects,and to reveal the coupling mechanism of roughness and interference effects on the riser,a VIV experiment of rough risers in tandem arrangement was conducted in a wave−current combined flume.The experiment characterized the risers’roughness by arranging different specifications of attachments on the surface of the risers.Three rough risers with different roughness and smooth risers were arranged in tandem arrangement,with the rough risers arranged downstream.The experimental results indicate that the suppression of the attachments on the downstream risers’vibration are more significant both in the CF and IL directions as the reduced velocity increases.For the downstream riser,the amplitude response of rough riser is more significantly weakened compared with the smooth one at high reduced velocity.For the upstream risers,changes in the roughness and spacing ratio have an impact on their‘lock-in’region.When the roughness of downstream risers is relatively large(0.1300)and the spacing between risers is small(S/D=4.0),the reduced velocity range of‘lock-in’region in the CF direction of upstream risers is obviously expanded,and the displacement in the‘lock-in’region is severer.展开更多
A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite ...A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite element method,the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law.The Van der Pol oscillator was used to simulate the effect of vortex shedding.The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm.The numerical model was verified with the published results.The VIV characteristics of the CTR subjected to uniform flows,including displacement,frequency,standing wave,traveling wave,motion trajectory,and energy transfer,were studied comprehensively.The numerical results revealed that the multimode property occurs in the CF-and IL-direction VIV responses of the CTR.An increase in the flow velocity has slight effects on the maximum VIV displacement.Due to structural nonlin-earity,the double-frequency relationship in the CF and IL directions is rarely captured.Therefore,the vibration trajectories display the shape of an inclined elliptical orbit.Moreover,the negative energy region is inconspicuous under the excitation of the uniform flow.展开更多
A series of numerical sinmlations about a small scale （aspect ratio： 63.2） flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration （VIV） have been taken into account. The wake hydrodyn...A series of numerical sinmlations about a small scale （aspect ratio： 63.2） flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration （VIV） have been taken into account. The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strat- egy designed for fluid-structure interaction （FSI） problem with well-performed LES model. The configuration of structured mesh, multi-domain design, different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case. The introduction of instantaneous amplitude definition and modeless component decom- position method （Chen and Kim, 2008） was helpful to reveal much more information from modal analysis. Most results from numerical simulation are generally consistent with those from model test （Choi and Hong, 2000） via the comparison between them. As supplementary to model test, visualization of the vortex wake was also provided. It has been proved that the forced oscillation doesn＇t only excite a complicated dumbbell-like wake pattern around the outer thimble, but also results in inner flow inside the PVC pipe. The velocity of the inner flow increases with the frequency of forced oscillation.展开更多
A unique oscillating wind-driven triboelectric nanogenerator(OWTENG)based on the sphere's vortex-induced vibration(VIV)behavior is proposed in this study,which can harvest wind energy across a multitude of horizon...A unique oscillating wind-driven triboelectric nanogenerator(OWTENG)based on the sphere's vortex-induced vibration(VIV)behavior is proposed in this study,which can harvest wind energy across a multitude of horizontal directions.With the Euler-Lagrange method,the coupled governing equations of the OWTENG are established and subsequently validated by experimental tests.The vibrational properties and output performance of the OWTENG for varying wind speeds are analyzed,demonstrating its effectiveness in capturing wind energy across a broad range of wind speeds(from 2.20 m/s to 8.84 m/s),and the OWTENG achieves its peak output power of 106.3μW at a wind speed of 5.72 m/s.Furthermore,the OWTENG maintains a steady output power across various wind directions within the speed range of 2.20 m/s to 7.63 m/s.Nevertheless,when the wind speed exceeds 7.63 m/s,the vibrational characteristics of the sphere shift based on the wind direction,leading to fluctuations in the OWTENG's output power.This research presents an innovative approach for designing vibrational triboelectric nanogenerators,offering valuable insights into harvesting wind energy from diverse directions and speeds.展开更多
In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
基金financially supported by the National Natural Science Foundation of China(Grant No.51779109)the Natural Science Foundation of Jiangsu Province(Grant No.BK20171306)
文摘A numerical simulation and an experimental study on vortex-induced motion（VIM） of a new type of deep draft multi-columns floating drilling production, storage and offloading（FDPSO） are presented in this paper. The main dimension, the special variable cross-section column and the cabin arrangement of the octagonal pontoon are introduced based on the result. The numerical simulation is adapted to study the effects of current incidence angles and reduced velocities on this platform’s sway motion response. The 300 m water depth equivalent truncated mooring system is adopted for the model tests. The model tests are carried out to check the reliability of numerical simulation. The results consist of surge, sway and yaw motions, as well as motion trajectories. The maximum sway amplitudes for different types of offshore platform is also studied. The main results show that the peak frequencies of sway motion under different current incidence angles and reduced velocities vary around the natural frequency. The analysis result of flow field indicates that the change of distribution of vortex in vertical presents significant influences on the VIM of platform. The trend of sway amplitude ratio curve of this new type FDPSO differs from the other types of platform. Under 45° current incidence angle, the sway amplitude of this new type of FDPSO is much smaller than those of other types of offshore platform at 4.4 ≤ V;≤ 8.9. The typical ‘8’ shape trajectory does not appear in the platform’s motion trajectories.
基金the National High Technology Research and Development Program (863) of China(No. 2006AA09A107)the Key Fundamental Research Project of Science and Technology Commission of Shanghai Municipality (No. 07XD14018)
文摘Spar platforms could be subject to vortex-induced-motions(VIM) in certain current conditions.Lockin is a phenomenon which occurs in a range of reduced velocities in VIM.In this paper,a new concept of spar platform called cell-truss spar is studied using both computational fluid dynamics(CFD) and model test to investigate the VIM of the spar under different reduced velocities.The unique configuration of the cell-truss spar is carefully considered,and the unsteady flow around the spar is calculated and visualized in CFD simulations.A physical model with a scale ratio of 1:100 of the cell-truss spar is fabricated,and model tests are carried out in the current-generating ocean engineering basin.Many important parameters in VIM of the cell-truss spar are obtained,the occurrence of lock-in phenomenon is successfully simulated,and the mechanism and rules of lock-in are analyzed.
基金Acknowledgements This work is supported by the National Natural Science Foundation of China （51490675, 51379125, 11432009, 51579145）, Chang Jiang Scholars Program （T2014099）, Shanghai Excellent Academic Leaders Program （17XD1402300）, Shanghai Key Laboratory of Marine Engineering （K2015-11）, Program for Professor of Special Appointment （Eastern Scholar） at Shanghai Institutions of Higher Learning （2013022）, Innovative Special Project of Numerical Tank of Ministry of Industry and Information Technology of China （2016-23/09） and Lloyd＇s Register Foundation for doctoral student, to which the authors are most grateful.
文摘This paper presents 3D （three-dimensional） CFD （computational fluid dynamic） simulation to analyse the FIR （flow-induced response） especially the yaw motion of a buoyancy can. The numerical cases are conducted with a buoyancy can under different reduced velocities utilizing our in-house code naoe-FOAM-SJTU, a solver based on the open source toolkit OpenFOAM. SST-DDES （shear-stress transport-delayed detached-eddy simulation） model is applied to handle the flowseparation and overset grid method is utilized to solve a large amplitude 6-DOF （6 degrees of freedom） motions. Free decay test and VIM （vortex-induced motion） test are built numerically. In VIM cases, the responses of trajectory, amplitude, frequency are calculated in a series of reduced velocities. With the increase of reduced velocity, yaw frequency is increased, which is similar to surge and sway frequency. And yaw frequency is equal to the sway frequency, which is consistent with experimental results. Furthermore, comparing two cases, one fixed in rotation and the other one free in rotation, it can be concluded that release in the degree of rotation can decrease the sway amplitude but make no difference in the surge amplitude.
基金supported by the National Natural Science Foundation of China(Grant No.51279104)a Research Project on High-Technology Ships by the Ministry of Industry and Information Technology
文摘A Deep Draft Semi-submersible （DDS） under certain flow conditions could be subjected to Vortex-Induced Motions （VIM）, which significantly influences the loads on and life fatigue of the moorings and the risers. To investigate the VIM of a DDS with four rectangular section columns in waves coupled with a uniform current, a numerical study using the computational fluid dynamics （CFD） method was conducted. The issues of the VIM of multi-column floaters can be con＇,＇eniently converted to the issues of oscillating cylinders in fluid cross flows. This paper looks into the CFD numerical simulation of infinite cylinders having rectangular sections in a two-dimensional sinusoidal time- dependent flow field coupled with a uniform current. The resulted hydrodynamic forces and motion responses in different oscillatory flows plus currents both aligned in the same direction for the incidence of 135° of the DDS relative to the flow are compared with the ones in current only cases. The results show that the VIM response of this geometric arrangement of a DDS with four rectangular columns in a current combined with oscillatory flows is more evident than that in the current only case. The oscillatory flows and waves have the significant influence on the VIM response, forces and trajectory, in-plane motions of the DDS.
基金supported by the National Natural Science Foundation of China(Grant No.51679138)the 1000 Young Talent Program(Grant No.15Z127060020)the National Basic Research Program of China(973 Program,Grant Nos.2015CB251203 and 2013CB036103)
文摘A phenomenological model for predicting the vortex-induced motion (VIM) of a single-column platform with non- linear stiffness has been proposed. The VIM model is based on the couple of the Duffing-van der Pol oscillators and the motion equations with non-linear terms. The model with liner stiffness is presented for comparison and their results are compared with the experiments in order to calibrate the model. The computed results show that the predicted VIM amplitudes and periods of oscillation are in qualitative agreements with the experimental data. Compared with the results with linear stiffness, it is found that the application of non-linear stiffness causes the significant reductions in the in-line and transverse motion amplitudes. Under the non-linear stiffness constraint, the lock-in behavior is still identified at 8<Ur<15, and the trajectories of the VIM on the xy plane with eight-figure patterns are maintained. The results with different non-linear geometrically parameters show that both in-line and transverse non-linear characteristics can significantly affect the predict in-line and transverse motion amplitudes. Furthermore, the computed results for different aspect ratios indicate that the in-line and transverse motion amplitudes increase with the growth of aspect ratio, and the range of lock-in region is enlarged for the large aspect ratio.
基金Supported by the National Natural Science Foundation of China (Grant No. 52222111)the National Science and Technology Major Project of China “Key Technologies and Equipment for Deepwater Dry Oil and Gas Production and Processing Platforms”(No. 2024ZD1403300)+1 种基金Subproject 5 “Research on Safety Risk Assessment Technology System for Deepwater Dry Oil and Gas Production and Processing Platforms”(No. 2024ZD1403305)the China Scholarship Council (202306440019)。
文摘A numerical simulation analysis is conducted to examine the unsteady hydrodynamic characteristics of vortex-induced vibration(VIV)and the suppression effect of helical strakes on VIV in subsea pipelines.The analysis uses the standard k−εturbulence model for 4.5-and 12.75-inch pipes,and its accuracy is verified by comparing the results with large-scale hydrodynamic experiments.These experiments are designed to evaluate the suppression efficiency of VIV with and without helical strakes,focusing on displacement and drag coefficients under different flow conditions.Furthermore,the influence of important geometric parameters of the helical strakes on drag coefficients and VIV suppression efficiency at different flow rates is compared and discussed.Numerical results agree well with experimental data for drag coefficient and vortex shedding frequency.Spring-pipe self-excited vibration experimental tests reveal that the installation of helical strakes substantially reduces the drag coefficient of VIV within a certain flow rate range,achieving suppression efficiencies exceeding 90%with strake heights larger than 0.15D.Notably,the optimized parameter combination of helical strakes,with a pitch of 15D,a fin height of 0.2D,and 45°edge slopes,maintains high suppression efficiency,thereby exhibiting superior performance.This study provides a valuable reference for the design and application of helical strakes and VIV suppression in subsea engineering.
基金financially supported by the National Key Research and Development Program of China(Grant No.2023YFC2811600)the National Natural Science Foundation of China(Grant Nos.52301349 and 52088102)+1 种基金the Qingdao Post-Doctorate Science Fund(No.QDBSH20220202070)the Major Scientific and Technological Innovation Project of Shandong Province(Grant No.2019JZZY010820).
文摘A deep-sea mining riser is a crucial component of the system used to lift seafloor mineral resources to the vessel.It is prone to damage and failure because of harsh environmental conditions and internal fluid erosion.Furthermore,damage can impact the response characteristics of the riser,but varying environmental loadings easily mask it.Thus,distin-guishing between riser damage and environmental effects poses a considerable challenge.To address this issue,a cantilevered model is created for a deep-sea mining riser via the concentrated mass method,and a time-domain analytical strategy is developed.The vortex-induced vibration(VIV)response characteristics of the riser are initially examined,considering various damage conditions and flow velocities.The study results revealed four primary observations:(a)effective tension can serve as a reliable indicator for identifying damage at lower velocities;(b)there are noticeable differences in displacement between the healthy and damaged risers in the in-line direction rather than the cross-flow direction;(c)frequency characteristics can more effectively distinguish the damage conditions at high flow velocities,with the mean square frequency and frequency variance being more effective than the centroid frequency and root variance frequency;(d)displacement differences are more sensitive to damage occurring near the top and bottom of the riser,while both velocity variations and structural damage can influence displacements,especially in regions between modal nodes.The vibrational behavior and damage indicators are clarified for structural health monitoring of deep-sea mining risers during lifting operations.
基金Supported by the National Natural Science Foundation of China(No.51905211)the“20 Regulations for New Universities”of Jinan(No.202228116).
文摘The position deviation of the underwater manipulator generated by vortex-induced vibration(VIV)in the shear flow increases relative to that in the uniform flow.Thus,this study established an experimental platform to investigate the vibration characteristics of the underwater manipulator under shear flow.The vibration response along the manipulator was obtained and compared with that in the uniform flow.Results indicated that the velocity,test height,and flow field were the main factors affecting the VIV of the underwater manipulator.With the increase in the reduced velocity(U_(r)),the dimensionless amplitudes increased rapidly in the in-line(IL)direction with a maximum of 0.13D.The vibration responses in the cross-flow(CF)and IL directions were concentrated at positions 2,3 and positions 1,2,with peak values of 0.46 and 0.54 mm under U_(r)=1.54,respectively.In addition,the vibration frequency increased with the reduction of velocity.The dimensionless dominant frequency in the CF and IL directions varied from 0.39-0.80 and 0.35-0.64,respectively.Moreover,the ratio of the CF and IL directions was close to 1 at a lower U_(r).The standard deviation of displacement initially increased and then decreased as the height of the test location increased.The single peak value of the standard deviation showed that VIV presented a single mode.Compared with the uniform flow,the maximum and average values of VIV displacement increased by 104%and 110%under the shear flow,respectively.
基金the financial support from National Key R&D Program of China(Grant number:2024YFC2815100)Natural Science Foundation of China(Grant number:52322110)Beijing Nova Program(Grant number:20230484341).
文摘Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce fatigue failure and even cause unpredictable drilling accidents.Therefore,it is important to study the ViV characteristics of deepwater drilling riser and reveal the main controlling factors for ensuring the safe and efficient operation of deepwater drilling engineering.In this paper,the ViV of deepwater drilling riser is numerically simulated in time domain based on the discrete vortex method(DvM).A hydrodynamic analysis model and governing equation of VIV is proposed with considering the effect of riser motion using DVM and slice method,where the governing equation is solved by Runge-Kutta method.Model validation is performed,which verified the correctness and accuracy of the mechanical model and the solution method.On this basis,the influence of the number of control points,current velocity,riser outer diameter,shear flow and top tension on the ViV characteristics of deepwater drilling risers are discussed in detail.The results show that with the increase of current velocity,the vibration amplitude of deepwater drilling riser decreases obviously,while the vibration frequency increases gradually.However,if the outer diameter of riser increases,the vibration amplitude increases,while the vibration frequency decreases gradually.The top tension also has great influence on the VIV of riser.When the top tension is 1.25 G,the VIV is suppressed to a certain extent.This study has guiding significance for optimal design and engineering control of deepwater drilling riser.
基金Projects(51925808,52078504,51822803) supported by the National Natural Science Foundation of ChinaProject(2022JJ10082) supported by the Natural Science Foundation of Hunan Province,China+1 种基金Project(N2022Z004) supported by the Research on Technology Development Trend and Key Common Problems in Railway,ChinaProject(Xplorer Prize 2021) supported by the Tencent Foundation,China。
文摘Installing the splitter plates is a passive aerodynamic solution for eliminating vortex-induced vibration (VIV). However, the influences of splitter plates on the VIV and aerostatic performances are more complicated due to aerodynamic interference between highway and railway decks. To study the effects of splitter plates, wind tunnel experiments for measuring VIV and aerostatic forces of twin decks under two opposite flow directions were conducted, while the surrounding flow and wind pressure of static twin decks with and without splitter plates are numerically simulated. The results showed that the incoming flow direction affects the VIV response and aerostatic coefficients. The highway deck has poor vertical and torsional VIV, and the VIV region and amplitude are different under different directions. While the railway deck only has vertical VIV when located upstream. The splitter plates can impede the process of vortex generation, shedding and impinging at the gap between twin deck, and significantly reducing the surface fluctuating pressure coefficient, thus effectively suppressing the VIV of twin decks. While, the splitter plates hurt the upstream deck regarding static wind stability and have little effect on the downstream deck. The splitter plates of appropriate width are recommended to improve VIV performances in twin parallel bridges.
基金the National Natural Science Foundation of China(Nos.52171316 and 51479116)。
文摘Vortex-induced vibration of hydrofoils is concerned with structural safety and noise level in hydraulic machinery and marine engineering.The research on vibration characteristics under different operating conditions is significant.In this study,numerical simulations are conducted to investigate the vortex-induced vibration responses of an elastically suspended hydrofoil with blunt trailing edge in pitch direction.The work studies the effects of four parameters,namely the structural natural frequency,mass ratio,initial attack angle,and Reynolds number on vibration characteristics,with special emphasis on frequency lock-in.Results indicate that as the structural natural frequency changes,the vibration amplitude may increase substantially within a certain frequency range,in which the vortex shedding frequency locks into the structural natural frequency,and frequency lock-in occurs.In addition,with increasing the mass ratio,the frequency range of lock-in becomes narrower,and both the upper and lower thresholds decrease.As the initial attack angle increases from 0◦to 6◦,the lock-in range gets reduced.Over the three Reynolds numbers(6×10^(5),9×10^(5),and 12×10^(5)),the lock-in range remains virtually unchanged.Moreover,for a certain structural natural frequency,modifying the mass ratio,initial attack angle,and Reynolds number could effectively suppress the vibration amplitude.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFC2806300)the National Natural Science Foundation of China(Grant No.52401338)+1 种基金supported by the State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University(Grant No.GKZD010089)the Development and Application Project of Ship CAE Software,and the Seed Foundation of Tianjin University.
文摘Vortex-induced vibration(VIV)of cylindrical structures is a critical fluid-structure interaction(FSI)phenomenon in ocean engineering.Simulating VIV accurately can be computationally expensive.This study presents a graphics processing unit(GPU)-accelerated simulation model for VIV utilizing the immersed boundary lattice Boltzmann method(IB-LBM),aiming to reduce computational costs while preserving accuracy.The program is developed using machine learning library JAX,which enables parallelism on GPU and multi-GPU platforms.The model incorporates multi-GPU parallelization and multi-block grid refinement strategies to enhance computational efficiency.Validation against existing high-fidelity simulation data demonstrates good agreement.Performance tests show significant speed-ups with GPU acceleration compared to traditional CPU-based approaches.These results underscore the potential of the developed simulator as an efficient and reliable tool for in-depth parametric studies and practical engineering analysis of VIV,facilitating more rapid design iterations and risk assessments for offshore structures.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51109158,U2106223)the Science and Technology Development Plan Program of Tianjin Municipal Transportation Commission(Grant No.2022-48)。
文摘When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.
基金supported by the Joint Postdoc Scheme with Non-local Institutions of the Hong Kong Polytechnic University(Grant No.1-YY4P).
文摘Biomimetic design has recently received widespread attention.Inspired by the Terebridae structure,this paper provides a structural form for suppressing vortex-induced vibration(VIV)response.Four different structural forms are shown,including the traditional smooth cylinder(P0),and the Terebridae-inspired cylinder with the helical angle of 30°(P_(30)),60°(P_(60)),and 90°(P_(90)).Computational fluid dynamics(CFD)method is adopted to solve the flow pass the Terebridae-inspired structures,and the vibration equation is solved using the Newmark-βmethod.The results show that for P_(30),P_(60) and P_(90),the VIV responses are effectively suppressed in the lock-in region,and P_(60) showed the best VIV suppression performance.The transverse amplitude and the downstream amplitude can be reduced by 82.67%and 91.43%respectively for P_(60) compared with that for P0,and the peak of the mean-drag coefficient is suppressed by 53.33%.The Q-criterion vortices of P_(30),P_(60),and P_(90) are destroyed,with irregular vortices shedding.It is also found that the boundary layer separation is located on the Terebridae-inspired ribs.The twisted ribs cause the separation point to constantly change along the spanwise direction,resulting in the development of the boundary layer separation being completely destroyed.The strength of the wake flow is significantly weakened for the Terebridae-inspired cylinder.
基金financially supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2023ME040 and ZR2022QE118)the Key Technology Research and Development Program of Shandong Province(Grant No.2023CXGC010316)+1 种基金the Natural Science Foundation of Qingdao(Grant No.23-2-1-207-zyyd-jch)the Introduction and Education Plan for Young Innovative talents in Colleges and Universities of Shandong Province(Marine Civil Engineering Materials and Structure Innovation Research Team).
文摘A vortex-induced vibration(VIV)experiment of rough risers with coupling interference effect under a side-by-side arrangement was carried out in a wave-current combined flume.The roughness of the riser was characterized by arranging different specifications of surface attachments on the surface of the riser.Rough risers with three different roughnesses were arranged side by side with smooth risers to explore the VIV response of the riser under the combined action of roughness and interference effect,and to reveal the coupling mechanism between roughness and interference effect.The experimental results show that,compared with that of a smooth riser,the VIV of a rough riser under the coupling interference effect has a wider"lock-in"region,and the displacement decreases more significantly at a high reduced velocity,which is more likely to excite higher-order modes and frequency responses.In addition,the displacement response and frequency response of the smooth riser are not significantly affected by wake interference from the rough riser,which is caused by the decrease of the wake region due to the delay of the boundary layer separation point of the rough riser.
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2023ME040 and ZR2022QE118)the Key Technology Research and Development Program of Shandong Province(Grant No.2023CXGC010316)the Natural Science Foundation of Qingdao(Grant No.23-2-1-207-zyyd-jch),and the National Natural Science Foundation of China(Grant No.51709161).
文摘In order to study the response law of vortex-induced vibration(VIV)of marine risers under the combined action of roughness and interference effects,and to reveal the coupling mechanism of roughness and interference effects on the riser,a VIV experiment of rough risers in tandem arrangement was conducted in a wave−current combined flume.The experiment characterized the risers’roughness by arranging different specifications of attachments on the surface of the risers.Three rough risers with different roughness and smooth risers were arranged in tandem arrangement,with the rough risers arranged downstream.The experimental results indicate that the suppression of the attachments on the downstream risers’vibration are more significant both in the CF and IL directions as the reduced velocity increases.For the downstream riser,the amplitude response of rough riser is more significantly weakened compared with the smooth one at high reduced velocity.For the upstream risers,changes in the roughness and spacing ratio have an impact on their‘lock-in’region.When the roughness of downstream risers is relatively large(0.1300)and the spacing between risers is small(S/D=4.0),the reduced velocity range of‘lock-in’region in the CF direction of upstream risers is obviously expanded,and the displacement in the‘lock-in’region is severer.
基金supported by the National Key R&D Program of China(No.2022YFB2602800)the National Science Foundation of China(No.51979257)+3 种基金the Basic Funding of the Central Public Research Institutes(Nos.TKS20210101,TKS20220103,TKS20230102)the Fundamental Research Funds for the Central Universities(No.202413018)the postdoctoral project of Shandong(No.SDCX-ZG-202400218)the postdoctoral project of Qingdao(No.QDBSH20240101013).
文摘A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite element method,the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law.The Van der Pol oscillator was used to simulate the effect of vortex shedding.The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm.The numerical model was verified with the published results.The VIV characteristics of the CTR subjected to uniform flows,including displacement,frequency,standing wave,traveling wave,motion trajectory,and energy transfer,were studied comprehensively.The numerical results revealed that the multimode property occurs in the CF-and IL-direction VIV responses of the CTR.An increase in the flow velocity has slight effects on the maximum VIV displacement.Due to structural nonlin-earity,the double-frequency relationship in the CF and IL directions is rarely captured.Therefore,the vibration trajectories display the shape of an inclined elliptical orbit.Moreover,the negative energy region is inconspicuous under the excitation of the uniform flow.
基金Korea Research Foundation Grant funded by the Korean Government (MOEHRD,Basic Research Promotion Fund) (KRF-2008-D00556)Mokpo National University RIC for Midisize Shipbuilding
文摘A series of numerical sinmlations about a small scale （aspect ratio： 63.2） flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration （VIV） have been taken into account. The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strat- egy designed for fluid-structure interaction （FSI） problem with well-performed LES model. The configuration of structured mesh, multi-domain design, different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case. The introduction of instantaneous amplitude definition and modeless component decom- position method （Chen and Kim, 2008） was helpful to reveal much more information from modal analysis. Most results from numerical simulation are generally consistent with those from model test （Choi and Hong, 2000） via the comparison between them. As supplementary to model test, visualization of the vortex wake was also provided. It has been proved that the forced oscillation doesn＇t only excite a complicated dumbbell-like wake pattern around the outer thimble, but also results in inner flow inside the PVC pipe. The velocity of the inner flow increases with the frequency of forced oscillation.
基金Project supported by the National Natural Science Foundation of China(Nos.12202151 and 12272140)。
文摘A unique oscillating wind-driven triboelectric nanogenerator(OWTENG)based on the sphere's vortex-induced vibration(VIV)behavior is proposed in this study,which can harvest wind energy across a multitude of horizontal directions.With the Euler-Lagrange method,the coupled governing equations of the OWTENG are established and subsequently validated by experimental tests.The vibrational properties and output performance of the OWTENG for varying wind speeds are analyzed,demonstrating its effectiveness in capturing wind energy across a broad range of wind speeds(from 2.20 m/s to 8.84 m/s),and the OWTENG achieves its peak output power of 106.3μW at a wind speed of 5.72 m/s.Furthermore,the OWTENG maintains a steady output power across various wind directions within the speed range of 2.20 m/s to 7.63 m/s.Nevertheless,when the wind speed exceeds 7.63 m/s,the vibrational characteristics of the sphere shift based on the wind direction,leading to fluctuations in the OWTENG's output power.This research presents an innovative approach for designing vibrational triboelectric nanogenerators,offering valuable insights into harvesting wind energy from diverse directions and speeds.
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
