Sag Bend Research Articles

Study on fatigue damage optimization mechanism of deepwater lazy wave risers based on multiple waveform serial arrangement

Lazy wave risers can mitigate the kinematic coupling between floating structure and riser touchdown zone (TDZ), so as to improve its fatigue life. However, due to the introduction of buoyancy blocks, nonlinear dynamic response and fatigue damage prediction will be more complicated. In this paper, a concept of “multiple lazy wave riser”, namely, deepwater lazy wave riser configuration based on multiple waveform serial arrangement, is proposed. According to the improved slender rod theory and equivalent optimization of buoyancy sections, three riser configurations with different heave excitations and currents are structured. The dynamic response characteristics, excitation motion transfer paths and fatigue damage hotspots are well compared. Moreover, the influence law of riser fatigue damage and decoupling mechanism of riser TDZ movements are also explored. The results indicate that: by constructing lazy wave configuration, deepwater risers based on lazy wave configuration can attenuate the kinematic coupled response of floating structure in the first sag bend section, and reduce the normal motion response in the riser TDZ, so as to optimize its anti-fatigue performance; compared with lazy wave riser, multiple lazy wave riser has some competitiveness in the anti-fatigue performance for the riser TDZ. For flexible risers, this competitiveness will become even more prominent.

Nonlinear riser-seabed interaction response among touchdown zone of a steel catenary riser in consideration of vortex-induced vibration

Steel catenary riser (SCR) is a preferred solution for deepwater oil and gas exploitation under harsh marine environment. Its riser-seabed interaction (RSI) among touchdown zone (TDZ) in consideration of the vortex-induced vibration (VIV) of sag bend is at present a research frontier in ocean engineering. This paper integrates Randolph-Quiggin model into a published global numerical riser model, to investigate the nonlinear RSI response among TDZ of an SCR with VIV. The adopted numerical model is validated against some published experimental measurements for VIV and RSI respectively. Three combined cases with top-end platform heave motion and VIV are simulated, and the trench development as well as the SCR's response characteristics among TDZ is analyzed. VIV makes the trench develop more smoothly, and the trench length as well as depth turns smaller. The VIV effect on RSI is relatively significant with violent heave excitation, under which the P-z curves present clearer interaction mode transitions. VIV enlarges the maximum bending moment visibly, and makes the sag bend of SCR dominated by higher-order modes, which are both detrimental to the structural safety. The coupling effect between RSI and VIV on the riser's dynamic response needs to be considered for the design of full-scale SCRs.

A tabular optimisation technique for steel lazy wave riser

Steel lazy wave riser (SLWR) is derived from the simple catenary riser (SCR) by the installation of buoyancy modules on its section. Infinite SLWR configurations are possible, and this poses difficulties in determining the best configuration. However, it is possible to capture some suitable configurations which satisfy some given design criteria specific to a project. We referred to these as the optimum configurations for the problem. Several advanced optimization tools and techniques for engineering optimization are available. In this paper, we present a 2D tabular optimization method for SLWR, which is an index-based optimization technique. The approach reduces a multidimensional problem to a 2D type providing a significant reduction in the required computational resources. It combines the design variables in pairs and assigns indices to the resulting design points (configurations) for each combination. The optimum design points are then tracked through index matching using techniques such as data sorting and intersection operations. In the application of the technique to SLWR design, we set the number of design variable for the problem to three. This results in three pair of combinations of the design variables. The design variables are the apparent mass ratio, the sag bend elevation, and the arc height. The output variables of interest to be optimized include the SLWR hanging length, the smeared buoyancy section length, the smeared buoyancy thickness, the riser hang-off tension, the stress utilization and fatigue damage around the bends. Selected optimum SLWR configurations from the optimization process are subjected to an irregular wave simulation to demonstrate the suitability of the approach for such optimisation problems.

Investigation of Antiadhesion Coatings for the Sag Bending of Silicate Glass

In the article, the features of the interaction of different forms of carbon with various solvents are investigated comprehensively, and the nature of defects and their effect on the optical and physicochemical properties of coatings are studied. The compositions of high-temperature antiadhesion parting mixtures for sag bending which are based on the high-temperature lubricants of carbon-containing materials are investigated. Base on the research, the mechanisms of the coagulation of particles during heat treatment, the effect of the structure and particle size of the studied mixtures on the coating quality, and the interaction with binders were studied, which made it possible to obtain high-temperature antiadhesion coatings with predetermined characteristics. The technology of applying these mixtures on the surface of glass billets and removing them from the glass surface, while meeting the environmental safety requirements, is developed.

Sag Bending Control in the Production of Automobile Windshields

Random inspection quality control of laminated windshields during sag molding was performed. The deviations from the technical specifications of the surface tensile stresses at the edge of the glass were revealed. Adaptive models describing the dependence of the tensile stresses at the glass edge on the sag bending temperature were constructed. An algorithm was developed for controlling the sag bending temperature. It is shown by means of simulation modeling that the magnitude of the surface tensile stresses in the produced articles can be stabilized.

The coupling VIV analysis of SCRs with rigid swing

With the development of deepwater oil and gas exploration, Steel Catenary Risers (SCRs) become preferred risers for resource production, import and export. Vortex induced vibration (VIV) is the key problem encountered in the design of SCRs. In this study, a new model, the rigid swing model, is proposed based on the consideration of large curvature of SCRs. The sag bend of SCRs is assumed as a rigid swing system around the axis from the hanging point to the touch down point (TDP) in the model. The torque, produced by the lift force and the swing vector, provides the driving torque for the swing system, and the weight of SCRs provides the restoring torque. The simulated response of rigid swing is coupled with bending vibration, and then the coupling VIV model of SCRs is studied in consideration of bending vibration and rigid motion. The calculated results indicate that the rigid swing has a magnitude equal to that of bending vibration, and the rigid motion affects the dynamic response of SCRs and can not be neglected in the VIV analysis.

An optimal control approach to an inverse nonlinear elastic shell problem applied to car windscreen design

A numerical procedure to optimise the sag bending process for car windscreens is proposed. In particular a simplified elastic model with geometric nonlinearities is considered. The optimisation approach is based on the numerical resolution of an optimal control problem in nonlinear elasticity. The objective of the optimisation is to match a desired shape by controlling the temperature distribution and minimising a quadratic functional. Also, we define and analyse the finite element approximation of the optimality system and a gradient method for the solution of the resulting discrete variational inequality. Finally, numerical experiments for the simulation of the simplified model are discussed.

A variational inequality formulation of an inverse elasticity problem

We present some systematic approaches to the mathematical formulation and numerical resolution of an optimal control problem in linear elasticity. The objective of the optimization is to match a desired displacement by controlling the Young's modulus so as to minimize a quadratic functional. Theoretical results are presented in the general framework of linear elastic theory which lead to a variational inequality. Also, we define and analyze a finite element approximation of the optimality system and a gradient method for the solution of the discrete variational inequality. Finally, numerical experiments for the simulation of a simplified model for the “sag bending process” in the manufacturing of automobile windscreens are discussed.

Dynamics of Suspended Marine Pipelines

As the development of offshore oil and gas production proceeds, the dynamic stresses in pipelines induced by laying operations become more important. The contribution of this paper is to the finite-element modelling of the dynamics of a large pipeline where nonlinear bottom reactions and ocean fluid drag are included. A time domain simulation procedure is described for computing the dynamic motion and stress response for arbitrary time history inputs at the surface. Also, a method of linearizing the seaway fluid drag terms and of handling the nonlinear bottom reactions is shown for harmonic seaway inputs. The two methods are compared and illustrate the reasonable accuracy of the linearized method. It is shown that dynamic bending stressess can be significant in the sag bend regions indicating the need for evaluation for future deep water applications. Additionally, it was found that dynamic bending stress magnitudes increased with ocean bottom rigidity. The model concentrates on the pipeline analysis and assumes a ramp-style stinger, the dynamics of which has not been included.