2011 Vol.(4)
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2011, (4): 549-564.
Abstract:
The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally. The typical phenomenon of the two-degree-of-freedom cylinder’s VIV is discussed. The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed. The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom. Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases. The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration. The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters. However, the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number.
The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally. The typical phenomenon of the two-degree-of-freedom cylinder’s VIV is discussed. The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed. The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom. Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases. The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration. The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters. However, the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number.
2011, (4): 565-575.
Abstract:
In this paper, flume experiments are focused on sediment transport inside and outside the surf zone. According to the energy dissipation balance principle of sediment-laden flow and the similarity between energy dissipation of spilling breaking wave and hydraulic jump, formulas are proposed to predict time averaged suspended sediment concentration under both non-breaking and breaking waves. Assuming that the sediment diffusion coefficient, which is related with energy dissipation, is proportional to water depth, formulas are proposed to predict close-to-bed suspended sediment concentration and vertical distribution of suspended sediment under spilling breaking waves, and the prediction shows a good agreement with the measurement.
In this paper, flume experiments are focused on sediment transport inside and outside the surf zone. According to the energy dissipation balance principle of sediment-laden flow and the similarity between energy dissipation of spilling breaking wave and hydraulic jump, formulas are proposed to predict time averaged suspended sediment concentration under both non-breaking and breaking waves. Assuming that the sediment diffusion coefficient, which is related with energy dissipation, is proportional to water depth, formulas are proposed to predict close-to-bed suspended sediment concentration and vertical distribution of suspended sediment under spilling breaking waves, and the prediction shows a good agreement with the measurement.
2011, (4): 577-590.
Abstract:
Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risers against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies, the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.
Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risers against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies, the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.
2011, (4): 591-608.
Abstract:
Storm surges are abnormal rises in sea level along coastal areas and are mainly formed by strong wind and atmospheric depressions. When storm surges coincide with high tide, coastal flooding can occur. Creating storm surge prediction systems has been an important and operational task worldwide. This study developed a coupled tide and storm surge numerical model of the seas around Taiwan for operational purposes at the Central Weather Bureau. The model was calibrated and verified by using tidal records from seas around Taiwan. Model skill was assessed based on measured records, and the results are presented in details. At 3-minute resolution, tides were generally well predicted, with the root mean-square errors of less than 0.11 m and an overall correlation of more than 0.9. Storms (winds and depressions) were introduced into the model forcing by using the parameter typhoon model. Five typical typhoons that threatened Taiwan were simulated for assessment. The surges were well predicted compared with the records.
Storm surges are abnormal rises in sea level along coastal areas and are mainly formed by strong wind and atmospheric depressions. When storm surges coincide with high tide, coastal flooding can occur. Creating storm surge prediction systems has been an important and operational task worldwide. This study developed a coupled tide and storm surge numerical model of the seas around Taiwan for operational purposes at the Central Weather Bureau. The model was calibrated and verified by using tidal records from seas around Taiwan. Model skill was assessed based on measured records, and the results are presented in details. At 3-minute resolution, tides were generally well predicted, with the root mean-square errors of less than 0.11 m and an overall correlation of more than 0.9. Storms (winds and depressions) were introduced into the model forcing by using the parameter typhoon model. Five typical typhoons that threatened Taiwan were simulated for assessment. The surges were well predicted compared with the records.
2011, (4): 609-624.
Abstract:
The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational
The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational
2011, (4): 625-643.
Abstract:
Accurate determination of flushing time is crucial for maintaining sustainable production in fish culture zones (FCZs), as it represents the physical self-purification capability via tidal exchange with clean water in the outer sea. However, owing to the temporal and spatial complexity of the coastal flushing process, existing methods for determining flushing time may not be generally applicable. In this paper, a systematic method for determining the flushing time in FCZs is presented, in which bathymetry, runoff, tidal range and stratification are properly accounted for. We determine the flushing time via numerical tracer experiments, using robust 3D hydrodynamic and mass transport models. For FCZs located in sheltered and land-locked tidal inlets, the system boundary can be naturally defined at the connection with the open sea. For FCZs located in open waters, hydrodynamic tracking is first used to assess the extent of tidal excursion and thus delimit the initial boundary between clean water and polluted water. This general method is applied to all designated marine FCZs in Hong Kong for both the dry and wet seasons, including 20 sheltered FCZs (in semi-enclosed waters of Tolo Harbour, Mirs Bay, and Port Shelter) and 6 FCZs in open waters. Our results show that flushing time is the longest in inner Port Shelter (about 40 days in dry season), and the shortest for the FCZs in open waters (less than one week in dry season). In addition, the flushing time in dry season is commonly longer than that in wet season: 20%~40% for most well-sheltered FCZs; 2.6~4 times for the others. Our results indicate a positive correlation between the flushing time and distance to open boundary, supporting the view that the flushing time of a FCZ is closely related to its location. This study provides a solid basis for mariculture management such as the determination of carrying capacity of FCZs.
Accurate determination of flushing time is crucial for maintaining sustainable production in fish culture zones (FCZs), as it represents the physical self-purification capability via tidal exchange with clean water in the outer sea. However, owing to the temporal and spatial complexity of the coastal flushing process, existing methods for determining flushing time may not be generally applicable. In this paper, a systematic method for determining the flushing time in FCZs is presented, in which bathymetry, runoff, tidal range and stratification are properly accounted for. We determine the flushing time via numerical tracer experiments, using robust 3D hydrodynamic and mass transport models. For FCZs located in sheltered and land-locked tidal inlets, the system boundary can be naturally defined at the connection with the open sea. For FCZs located in open waters, hydrodynamic tracking is first used to assess the extent of tidal excursion and thus delimit the initial boundary between clean water and polluted water. This general method is applied to all designated marine FCZs in Hong Kong for both the dry and wet seasons, including 20 sheltered FCZs (in semi-enclosed waters of Tolo Harbour, Mirs Bay, and Port Shelter) and 6 FCZs in open waters. Our results show that flushing time is the longest in inner Port Shelter (about 40 days in dry season), and the shortest for the FCZs in open waters (less than one week in dry season). In addition, the flushing time in dry season is commonly longer than that in wet season: 20%~40% for most well-sheltered FCZs; 2.6~4 times for the others. Our results indicate a positive correlation between the flushing time and distance to open boundary, supporting the view that the flushing time of a FCZ is closely related to its location. This study provides a solid basis for mariculture management such as the determination of carrying capacity of FCZs.
2011, (4): 645-656.
Abstract:
The wave transmission characteristics and wave induced pressures on twin plate breakwater are investigated experimentally in regular and random waves. A total of twenty pressure transducers are fixed on four surfaces of twin plate to measure the wave induced dynamic pressures. The spatial distribution of dynamic wave pressure is given along the surface of the twin plate. The uplift wave force obtained by integrating the hydrodynamic pressure along the structure is presented. Discussed are the influence of different incident wave parameters including the relative plate width , relative wave height and relative submergence depth on the non-dimensional dynamic wave pressures and total wave forces. From the investigation, it is found that the optimum transmission coefficient, occurs around , and the twin plate breakwater is more effective in different water depths. The maximum of pressure ratio decreases from 1.8 to 1.1 when the relative submergence depth of top plate is increased from to +0.8.
The wave transmission characteristics and wave induced pressures on twin plate breakwater are investigated experimentally in regular and random waves. A total of twenty pressure transducers are fixed on four surfaces of twin plate to measure the wave induced dynamic pressures. The spatial distribution of dynamic wave pressure is given along the surface of the twin plate. The uplift wave force obtained by integrating the hydrodynamic pressure along the structure is presented. Discussed are the influence of different incident wave parameters including the relative plate width , relative wave height and relative submergence depth on the non-dimensional dynamic wave pressures and total wave forces. From the investigation, it is found that the optimum transmission coefficient, occurs around , and the twin plate breakwater is more effective in different water depths. The maximum of pressure ratio decreases from 1.8 to 1.1 when the relative submergence depth of top plate is increased from to +0.8.
2011, (4): 657-667.
Abstract:
Underwater vehicle plays an important role in ocean engineering. Depth control by fin is one of the difficulties for underwater vehicle in motion control. Depth control is indirect due to the freedom coupling between trim and axial motion. It includes the method of dynamic analysis and lift-resistance-coefficient experiment and theory algorithm. By considering the current speed and depth deviation, comprehensive interpretation is used in object-planning instruction. Expected depth is transformed into expected trim. Dynamic output fluctuation can be avoided, which is caused by linear mapping of deviation. It is steady and accurate for the motion of controlled underwater vehicles. The feasibility and efficiency of the control method are testified in the pool and natural area for experiments.
Underwater vehicle plays an important role in ocean engineering. Depth control by fin is one of the difficulties for underwater vehicle in motion control. Depth control is indirect due to the freedom coupling between trim and axial motion. It includes the method of dynamic analysis and lift-resistance-coefficient experiment and theory algorithm. By considering the current speed and depth deviation, comprehensive interpretation is used in object-planning instruction. Expected depth is transformed into expected trim. Dynamic output fluctuation can be avoided, which is caused by linear mapping of deviation. It is steady and accurate for the motion of controlled underwater vehicles. The feasibility and efficiency of the control method are testified in the pool and natural area for experiments.
2011, (4): 669-678.
Abstract:
A structure function approach is applied to estimate the turbulent kinetic energy (TKE) dissipation rate in the bottom boundary layer of the Pearl River Estuary (PRE). Simultaneous measurements with an acoustic Doppler velocimeter (ADV) supplied independent data for the verification of the structure function method. The results show that, 1) the structure function approach is reliable and successfully applied method to estimate the TKE dissipation rate. The observed dissipation rates range between 8.3×10?4 W/kg and 4.9×10?6 W/kg in YM01 and between 3.4×10?4 W/kg and 4.8×10?7 W/kg in YM03, respectively, while exhibiting a strong quarter-diurnal variation. 2) The balance between the shear production and viscous dissipation is better achieved in the straight river. This first-order balance is significantly broken in the estuary by non-shear production/dissipation due to wave-induced fluctuations.
A structure function approach is applied to estimate the turbulent kinetic energy (TKE) dissipation rate in the bottom boundary layer of the Pearl River Estuary (PRE). Simultaneous measurements with an acoustic Doppler velocimeter (ADV) supplied independent data for the verification of the structure function method. The results show that, 1) the structure function approach is reliable and successfully applied method to estimate the TKE dissipation rate. The observed dissipation rates range between 8.3×10?4 W/kg and 4.9×10?6 W/kg in YM01 and between 3.4×10?4 W/kg and 4.8×10?7 W/kg in YM03, respectively, while exhibiting a strong quarter-diurnal variation. 2) The balance between the shear production and viscous dissipation is better achieved in the straight river. This first-order balance is significantly broken in the estuary by non-shear production/dissipation due to wave-induced fluctuations.
2011, (4): 679-686.
Abstract:
Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schr?dinger equation (NLS). However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral (HOS) method, which can be applied for the direct phase-resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer’s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details
Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schr?dinger equation (NLS). However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral (HOS) method, which can be applied for the direct phase-resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer’s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details
2011, (4): 687-697.
Abstract:
In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green’s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step (n-1)Δt to nΔt , the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is established, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.
In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green’s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step (n-1)Δt to nΔt , the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is established, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.
2011, (4): 699-708.
Abstract:
The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is found that: 1) The efficient wave exciting force exists while plate submergence is less than 0.5 m, and the plate is very thin with order O(0.005 m). 2) The maximum heave wave exciting force exists, and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored. 3) The maximum sway wave exciting force exists, it is the main factor for surface or submerged vertical plate, and the roll force is about 20 times of horizontal plate.
The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is found that: 1) The efficient wave exciting force exists while plate submergence is less than 0.5 m, and the plate is very thin with order O(0.005 m). 2) The maximum heave wave exciting force exists, and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored. 3) The maximum sway wave exciting force exists, it is the main factor for surface or submerged vertical plate, and the roll force is about 20 times of horizontal plate.
2011, (4): 709-720.
Abstract:
As the exploration and exploitation of oil and gas proliferate throughout deepwater area, the requirements on the reliability of dynamic positioning system become increasingly stringent. The control objective ensuring safety operation at deep water will not be met by a single controller for dynamic positioning. In order to increase the availability and reliability of dynamic positioning control system, the triple redundancy hardware and software control architectures were designed and developed according to the safe specifications of DP-3 classification notation for dynamically positioned ships and rigs. The hardware redundant configuration takes the form of triple-redundant hot standby configuration including three identical operator stations and three real-time control computers which connect each other through dual networks. The function of motion control and redundancy management of control computers were implemented by software on the real-time operating system VxWorks. The software realization of task loose synchronization, majority voting and fault detection were presented in details. A hierarchical software architecture was planed during the development of software, consisting of application layer, real-time layer and physical layer. The behavior of the DP-3 dynamic positioning control system was modeled by a Markov model to analyze its reliability. The effects of variation in parameters on the reliability measures were investigated. The time domain dynamic simulation was carried out on a deepwater drilling rig to prove the feasibility of the proposed control architecture
As the exploration and exploitation of oil and gas proliferate throughout deepwater area, the requirements on the reliability of dynamic positioning system become increasingly stringent. The control objective ensuring safety operation at deep water will not be met by a single controller for dynamic positioning. In order to increase the availability and reliability of dynamic positioning control system, the triple redundancy hardware and software control architectures were designed and developed according to the safe specifications of DP-3 classification notation for dynamically positioned ships and rigs. The hardware redundant configuration takes the form of triple-redundant hot standby configuration including three identical operator stations and three real-time control computers which connect each other through dual networks. The function of motion control and redundancy management of control computers were implemented by software on the real-time operating system VxWorks. The software realization of task loose synchronization, majority voting and fault detection were presented in details. A hierarchical software architecture was planed during the development of software, consisting of application layer, real-time layer and physical layer. The behavior of the DP-3 dynamic positioning control system was modeled by a Markov model to analyze its reliability. The effects of variation in parameters on the reliability measures were investigated. The time domain dynamic simulation was carried out on a deepwater drilling rig to prove the feasibility of the proposed control architecture
2011, (4): 721-736.
Abstract:
Underwater gliders, which glide through water columns by use of a pair of wings, are efficient long-distance, long-duration marine environment observatory platforms. The Sea-Wing underwater glider, developed by the Shenyang Institute of Automation, CAS, is designed for the application of deep-sea environment variables observation. The system components, the mechanical design, and the control system design of the Sea-Wing underwater glider are described in this paper. The pitch and roll adjusting models are derived based on the mechanical design, and the adjusting capabilities for the pitch and roll are analyzed according to the models. Field experiments have been carried out for validating the gliding motion and the ability of measuring ocean environment variables. Experimental results of the motion performances of the glider are presented.
Underwater gliders, which glide through water columns by use of a pair of wings, are efficient long-distance, long-duration marine environment observatory platforms. The Sea-Wing underwater glider, developed by the Shenyang Institute of Automation, CAS, is designed for the application of deep-sea environment variables observation. The system components, the mechanical design, and the control system design of the Sea-Wing underwater glider are described in this paper. The pitch and roll adjusting models are derived based on the mechanical design, and the adjusting capabilities for the pitch and roll are analyzed according to the models. Field experiments have been carried out for validating the gliding motion and the ability of measuring ocean environment variables. Experimental results of the motion performances of the glider are presented.
2011, (4): 737-746.
Abstract:
The unbonded flexible pipe of eight layers, in which all the layers except the carcass layer are assumed to have isotropic properties, has been analyzed. Specifically, the carcass layer shows the orthotropic characteristics. The effective elastic moduli of the carcass layer have been developed in terms of the influence of deformation to stiffness. With consideration of the effective elastic moduli, the structure can be properly analyzed. Also the relative movements of tendons and relative displacements of wires in helical armour layer have been investigated. A three-dimensional nonlinear finite element model has been presented to predict the response of flexible pipes under axial force and torque. Further, the friction and contact of interlayer have been considered. Comparison between the finite element model and experimental results obtained in literature has been given and discussed, which might provide practical and technical support for the application of unbonded flexible pipes.
The unbonded flexible pipe of eight layers, in which all the layers except the carcass layer are assumed to have isotropic properties, has been analyzed. Specifically, the carcass layer shows the orthotropic characteristics. The effective elastic moduli of the carcass layer have been developed in terms of the influence of deformation to stiffness. With consideration of the effective elastic moduli, the structure can be properly analyzed. Also the relative movements of tendons and relative displacements of wires in helical armour layer have been investigated. A three-dimensional nonlinear finite element model has been presented to predict the response of flexible pipes under axial force and torque. Further, the friction and contact of interlayer have been considered. Comparison between the finite element model and experimental results obtained in literature has been given and discussed, which might provide practical and technical support for the application of unbonded flexible pipes.
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