The Lift Forces Acting on a Submarine Composite Pipeline in a Wave-Current Coexisting Field

- A composite pipeline is defined as a main big pipe composed of one or several small pipes. The flow behaviour around a submarine composite pipeline is more complicated than that around a single submarine pipeline. A series model test of composite pipelines in a wave-current coexisting field was conducted by the authors. Both in-line and lift forces were measured, and the resultant forces were also analyzed. The results of lift forces and resultant forces are reported in this paper. It is found that the lift force coefficients for composite pipelines are well related to the KC number. The lift force coefficients for an irregular wave-current coexisting field are smaller than those for a regular wave-current coexisting field. The frequency of lift force is usually twice the wave frequency or higher. The authors test indicates that the resultant forces are about 10 to 20 percent larger than in-line forces (horizontal forces). The effect of water depth is analyzed. Finally, the relationship between lift f     

Normalization of Hydrodynamic Coefficients in Morison Equation

-The hydrodynamic coefficients C_d and C_m are not only dependent on the size of slender cylin-der,its location in water,KC number and Re number,but also vary with environmental conditions,i.e.,in regular waves or in irregular waves,in pure waves or in wave-current coexisting field.In this paper,thenormalization of hydrodynamic coefficients for various environmental conditions is discussed.When aproper definition of KC number and proper characteristic values of irregular waves are used,a unified re-lationship between C_d,C_m and KC number for regular waves,irregular waves,pure waves and wave-cur-rent coexisting field can be obtained.     

Wave-Current Forces on Small Square Cylinders (Part I)

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.     

Wake model of hydrodynamic forces on pipelines

The hydrodynamic force model for pipelines presented includes flow history effects (wake effects) and time dependence in the force coefficients. These two features in the model were necessary to obtain satisfactory agreement between model predictions and full scale field measurements of pipeline forces. Conventional force models which represent adaptations of Morison's equation with ambient velocity and constant coefficients give predictions which for the lift component of the force in particular are in very poor agreement with the measurements. The parameters in the new model have been estimated on the basis of the full scale measurements and reflect a wide range of flow conditions. The model can be used in pipeline on-bottom stability design calculations for regular or irregular waves.     

Inline forces on vertical pile in irregular waves

The total inline wave forces, the irregular wave forces in particular, on an isolated pile are investigated by experiment. The relationships between force coefficients Cd and CM including in Morison's Eq. . and KC number or Reynolds number Re, and the variation of Cd and Cm in frequency domain are analysed with the method of least-squares in time domain and that of cross-spectral analysis. The plots of C4and Cmversus KCare given for both regular and irregular waves and those for irregular waves are used for numerical simulation of the irregular wave forces on the vertical pile and the results are in fairly good agreement with the test data. Based on the experimental results , the applicability of the spectral analysis method for calculating irregular wave forces on an isolated pile is investigated with the coherency γ between wave and wave forces and with KC number.     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

Hydrodynamic Forces and Instability of Submarine Pipelines Under Waves and Currents： A Review

Stability design of submarine pipelines is a very important procedure in submarine pipeline engineering design. The calculation of hydrodynamic forces caused by waves and currents acting on marine pipelines is an essential step in pipeline design for stability. The hydrodynamic forces-induced instabilities of submarine pipelines should be regarded as a wave/ current-pipeline-seabed interaction problem. This paper presents a review on hydrodynamic forces and stability research of submarine pipelines under waves and currents. The representative progress including the improved design method and guideline has been made for the marine pipelines engineering design through experimental investigations, numerical simulations and analytical models. Finally, further studies on this issue are suggested.     

波流共同作用下海底子母管线水动力的物理模型试验研究

通过物理模型试验研究海底子母管线分别在规则波加流和不规则波加流作用下的水动力特性。基于Morison方程,采用"等效直径法"分析得到子母管线拖曳力系数C_D,惯性力系数C_M和升力系数C_L(C_D+,C_L-)。试验分别考察了流速比U_c/U_w,母管与海床间隙比e/D及子母管间的相对缝隙G/D对海底子母管线水动力系数的影响。结果表明水动力系数随U_c/U_w的增大而减小;当e/D<0.5时,海床对子母管线受力的影响比较明显,C_D,C_M及C_L+均随e/D增大而减小,|C_L-|随e/D增大而增大;对子母管间的相互影响也不可忽略,C_D,C_M和|C_L-|均随G/D增大而减小,C_L+值随G/D增大而增大。     

波流共同作用下海底子母管线水动力的物理模型试验研究

通过物理模型试验研究海底子母管线分别在规则波加流和不规则波加流作用下的水动力特性。基于Morison方程,采用"等效直径法"分析得到子母管线拖曳力系数C_D,惯性力系数C_M和升力系数C_L(C_D⁺,C_L^-)。试验分别考察了流速比U_c/U_w,母管与海床间隙比e/D及子母管间的相对缝隙G/D对海底子母管线水动力系数的影响。结果表明水动力系数随U_c/U_w的增大而减小;当e/D<0.5时,海床对子母管线受力的影响比较明显,C_D,C_M及C_L⁺均随e/D增大而减小,|C_L^-|随e/D增大而增大;对子母管间的相互影响也不可忽略,C_D,C_M和|C_L^-|均随G/D增大而减小,C_L⁺值随G/D增大而增大。     

Hydrodynamic Coefficients for Grouping Piles Under the Action of Irregular Waves

-The hydrodynamic coefficients for each of two piles and three piles in both side-by-side arrangement and tandem arrangement under the action of irregular waves are experimentally investigated. These coefficients vary with the KC number, the relative pile spacing, the number of piles and the pile location, and their relationships are presented in this paper. They can be used in Morison Equation and other equations to calculate directly the in-line wave forces and the transverse forces on each pile in array.     

Wave-Current Forces on Small Square Cylinders (Part II)

Based on model tests, the lift and resultant forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in this paper. The lift and resultant force coefficients CL and Cf related to KC number and the effect of direction of wave propagation are also given, which may be useful for practical engineering application.     

Experimental Study on Conversion Efficiency of A Floating OWC Pentagonal Backward Bent Duct Buoy Wave Energy Converter

Wave tank tests were carried out to evaluate the total efficiency of a floating OWC Pentagonal Backward Bent Duct Buoy (PBBDB). Two kinds of turbine generators were used in tests. The incident wave power, pneumatic power and electricity were measured. The test results show that the primary efficiency can reach up to 185.98% in regular waves and 85.86% in irregular waves. The total efficiency from wave to wire with Wells turbine-generator set is 33.43% in regular waves and 15.82% in irregular waves. The peak total efficiency of the PBBDB with check valves equipped with the impulse turbine-generator set is 41.68% in regular waves and 27.10% in irregular waves. The efficiency of the turbine-generator set is about 30% in the tests. Obviously, the total efficiency can be further improved with the increasing of turbine efficiency.     

Experimental study of the hydrodynamic performance of an onshore wave power device in the presence of an underwater mound

The hydrodynamic functioning of an oscillating water column (OWC) in the presence of an underwater tri-dimensional mound (UTDM) through large-scale ocean engineering basin experiments is described. Experiments are carried out with both regular and irregular waves and are compared to numerical models. The analysis is based on the measurements of the wave amplification in the water column for the OWC performance and on surface deformation upwave and over the UTDM for the wave transformation due to both UTDM and OWC. A significant increase of the capture-width ratio due to wave focusing above the mound is observed experimentally. This wave focusing is also well described numerically with a refraction–diffraction model. The wave amplification in the water column for both regular and irregular waves is compared to results from a linear potential model based on an integral matching method. Linear behaviour of the hydrodynamic response of the device is verified for both open and partially closed conditions, in particular for irregular waves.     

Exact solution and approximate solution of irregular wave radiation stress for non-breaking wave

Wave radiation stress is the main driving force of wave-induced near-shore currents. It is directly related to the hydrodynamic characteristics of near-shore current whether the calculation of wave radiation stress is accurate or not. Irregular waves are more capable of reacting wave motion in the ocean compared to regular waves.Therefore, the calculation of the radiation stress under irregular waves will be more able to reflect the wave driving force in the actual near-shore current. Exact solution and approximate solution of the irregular wave radiation stress are derived in this paper and the two kinds of calculation methods are compared. On the basis of this, the experimental results are used to further verify the calculation of wave energy in the approximate calculation method. The results show that the approximate calculation method of irregular wave radiation stress has a good accuracy under the condition of narrow-band spectrum, which can save a lot of computing time, and thus improve the efficiency of calculation. However, the exact calculation method can more accurately reflect the fluctuation of radiation stress at each moment and each location.     

Water surface resonance in the L-shaped channel of seawater exchange breakwater

The resonance period of the L-shaped channel in the caisson is predicted analytically for the seawater exchange breakwater of “Applicability Study of the Seawater Exchange Breakwater (1). Korea Ministry of Maritime Affairs and Fisheries (in Korean) (1999a)”. Hydraulic experiments are conducted for a composite breakwater with a rear reservoir that is one of the seawater exchange breakwaters developed by them. For regular waves, the water surface elevation in the channel and the flow rate through the breakwater are measured. For irregular waves, the flow rate through the breakwater and the reflection coefficient on the breakwater are measured. The resonant maximum values in both the surface elevation and the flow rate, and the resonant minimum values in the reflection coefficient are all at wave periods slightly longer than analytically predicted ones. The measured resonance period for irregular waves is closer to the predicted one than for regular waves. If the resonance period of the L-shaped channel is fitted to the dominant period of incident waves, there would be high efficiency of seawater exchange between inside and outside the harbor.     

Hilbert Transferin Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improveraent of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda s method and satisfactory results are obtained.     

Hilbert Transform Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient.The reflection performance of the physical model can be estimated exactly without calculation of wave height and phasedifference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda‘s method and satisfactory results are obtained.     

Wave forces on large offshore pipelines

A laboratory investigation of wave forces induced by a regular train of waves on a large pipeline resting on the bed and at various clearances from the bed is presented. From considerations of dimensional analysis horizontal and vertical components of wave forces acting on the pipeline are expressed as force coefficients which are shown to be functions mainly of H/2a, gT²/2a, d/a and e/2a. A simple unseparated flow model based on potential flow theory and Morison's equation is presented for evaluating the maximum forces on the pipeline. The experimental results are com3ared with the theoretical results and data from existing literature. Based on the experimental results, hydrodynamic coefficients C_M and C_L have been evaluated     

Stochastic analysis of the second-order hydrodynamic quantities for offshore structures

The present study considers the prediction of extreme values of the second-order hydrodynamic parameters related to offshore structures in waves, where the application of Gaussian distribution is not valid. Particularly, this study focuses on a characteristic function approach in the frequency domain to estimate the probability distribution of the second-order quantities, and the results are compared with direct simulations in the time domain. The stochastic behaviors of the second-order hydrodynamic quantities are investigated with the characteristic function approach, which involves eigenvalue analyses of Hermitian kernels constructed with quadratic transfer functions. Three different second-order responses are considered: the springing responses of TLP tendons representative of the sum-frequency problem, the slow-drift motions of a semi-submersible platform moored in waves as a representative of the difference-frequency problem, and the wave run-up around a vertical column for regular and irregular waves. The applicability of the present approach in predicting extreme values is assessed by comparing the results with the values obtained from time-domain signals.     

海底管道掏空与波浪力变化关系试验

鉴于海底油气管道在海洋能源开发中的特殊意义,前人开展了大量管道安全试验研究,特别注重不同底床、不同波浪条件、不同埋置深度等方面的组合试验,本次试验针对危害管道安全的掏空和悬跨开展了波浪水槽试验,探讨黄河三角洲为主的粉土海床上掏空与管道受力关系,弥补这方面研究的不足,结果表明,海底管道受力变化与掏空过程密切相关。连续试验过程表明,海底管道与海床土、波浪水体之间存在密切关系。海底管道在波浪作用下冲刷掏空经历了3个演变阶段:泥沙起动阶段、水流隧道发育阶段、快速掏空阶段和冲刷平衡阶段。水流隧道伴随的管涌对冲刷掏空起重要作用。伴随冲刷掏空,管道波浪力出现规律性转化,从正向作用逐渐过渡到负向作用,也可以分出4个演化阶段:冲刷初始阶段,管道波浪力以正向为主,管道表现为正向力作用下的振动;隧道发育阶段,管道受到的作用力主要是波峰上举力和波谷下拉力,表现为上下振动;管道悬空阶段,波峰负向作用力和波谷正向力交替出现,管道在波浪作用下表现为前后振动;冲刷平衡阶段,管道主要在负向作用力下振动。