A Geophysical Flow Experiment in a Compressible Critical Fluid

The first objective of this experiment is to build an experimental system in which, in analogy to a geophysical system, a compressible fluid in a spherical annulus becomes radially stratified in density through an A.C. electric field. When this density gradient is demonstrated, the system will be augmented so that the fluid can be driven by heating and rotation and tested in preparation for a microgravity experiment. This apparatus consists of a spherical capacitor filled with critical fluid in a temperature controlled environment. To make the fluid critical, the apparatus will be operated near the critical pressure, critical density, and critical temperature of the fluid. This will result in a highly compressible fluid because of the properties of the fluid near its critical point. A high voltage A.C. source applied across the capacitor will create a spherically symmetric central force because of the dielectric properties of the fluid in an electric field gradient. This central force will induce a spherically symmetric density gradient that is analogous to a geophysical fluid system. To generate such a density gradient the system must be small (approx. 1 inch diameter). This small cell will also be capable of driving the critical fluid by heating and rotation. Since a spherically symmetric density gradient can only be made in microgravity, another small cell, of the same geometry, will be built that uses incompressible fluid. The driving of the fluid by rotation and heating in these small cells will be developed. The resulting instabilities from the driving in these two systems will then be studied. The second objective is to study the pattern forming instabilities (bifurcations) resulting from the well controlled experimental conditions in the critical fluid cell. This experiment will come close to producing conditions that are geophysically similar and will be studied as the driving parameters are changed

Growth and Morphology of Phase Separating Supercritical Fluids

The scientific objective is to study the relation between the morphology and the growth kinetics of domains during phase separation. We know from previous experiments performed near the critical point of pure fluids and binary liquids that there are two simple growth laws at late times. The 'fast' growth appears when the volumes of the phases are nearly equal and the droplet pattern is interconnected. In this case the size of the droplets grows linearly in time. The 'slow' growth appears when the pattern of droplets embedded in the majority phase is disconnected. In this case the size of the droplets increases in proportion to time to the power 1/3. The volume fraction of the minority phase is a good candidate to determine this change of behavior. All previous attempts to vary the volume fraction in a single experimental cell have failed because of the extreme experimental difficulties

Temporal Modulation of Traveling Waves in the Flow Between Rotating Cylinders With Broken Azimuthal Symmetry

The effect of temporal modulation on traveling waves in the flows in two distinct systems of rotating cylinders, both with broken azimuthal symmetry, has been investigated. It is shown that by modulating the control parameter at twice the critical frequency one can excite phase-locked standing waves and standing-wave-like states which are not allowed when the system is rotationally symmetric. We also show how previous theoretical results can be extended to handle patterns such as these, that are periodic in two spatial direction.Comment: 17 pages in LaTeX, 22 figures available as postscript files from http://www.esam.nwu.edu/riecke/lit/lit.htm

Efficient Modelling and Design Optimization of Large Floating Wind Turbines

Floating wind turbines (FWTs) are considered a promising solution for wind energy harvesting in deep water, but are currently too expensive to compete with other energy sources. Being a relatively new and immature technology means that there still is a large potential for cost reductions through optimization of the FWT structure. Optimized designs will bring the construction costs of FWTs down and increase profitability, which is currently the major challenge for the industry. Optimized designs can also result in increased reliability, which is an important issue. The main purpose of this work was to improve the design process for FWTs and thus contribute to reducing the cost of energy. This is addressed through two overall research objectives, which consider i) increased computational efficiency of global design analyses for FWTs, and ii) methods for numerical iii iv design optimization which can help identify cost-effective and reliable design solutions. The main focus was on the support structure and controller for 10 MW spar-type turbines, considering fatigue and ultimate loads. A linearized aero-hydro-servo-elastic model was shown to yield good results for the fatigue loads in the support structure. Acceptable agreement was also observed for short-term extreme response, especially for the support structure bending moments, which were quite Gaussian also in harsh environmental conditions. The resonant platform pitch response was overestimated by the linear model, especially in near-rated conditions. A gradient-based optimization approach with analytic derivatives was developed to perform integrated design optimization of the support structure, blade-pitch controller, and mooring system for an elastic 10 MW spar FWT, including the scantling design of the hull, where the goal was to minimize a combination of design costs and rotor speed variation. Different control strategies were compared through integrated design of the controller and support structure, which allowed for identification of optimal control parameters in a lifetime perspective, and fair comparisons between different strategies. The impact of environmental modelling on the long-term fatigue reliability, and associated design costs, of the support structure was also assessed through re-design of the tower and platform. The methodologies for global response analyses and integrated design optimization developed in the present work have been shown to be suitable for preliminary design of spar FWTs, where they can provide a starting design for later and more detailed design phases. Different modelling and design aspects for cost-effective and reliable solutions have been identified and assessed. The methodologies can be further extended to account for different FWT concepts, additional design parameters, and other load cases, and may help identify novel design solutions

Assessment of Uncertainties in Estimated Wellhead Fatigue

During subsea drilling, the motions of the Mobile Offshore Drilling Unit (MODU) and riser cause cyclic bending moments on the wellhead. This may lead to fatigue failure of the component, which can have severe consequences, and there are currently no international standards on how to carry out a wellhead fatigue damage assessment. Through the Joint Industry Project (JIP) Structural Well Integrity, a general wellhead fatigue analysis method has recently been proposed, where the fatigue damage is estimated from a global and a local finite element analysis. There are however several uncertainties regarding the modelling of the systems, which can have significant effects on the estimated fatigue life. In this thesis, some of these uncertainties are identified, and their effect on wellhead fatigue is studied.A short description of a typical subsea drilling system is given, and relevant theory on the topic is presented. The theory consists of an introduction to dynamic response analyses of risers and fatigue life calculations for marine structures, as well as a summary of the general wellhead fatigue analysis method described in the current method.A global riser model is established in Sima/Riflex, which is a software developed for analysis of slender marine structures. A local wellhead system model is also established in the finite element program Abaqus, and the fatigue damage in a typical North Sea well is assessed for a one year long historical operation. The first uncertainty to be studied is the modelling of interaction between conductor and soil. This is usually done using p-y curves, which relate the lateral pressure from the soil to the displacement of the structure. The method describes how to construct p-y curves for both static and cyclic loads, where the static curves are commonly used. In this thesis, the analyses are also conducted with cyclic soil springs. Another modelling aspect with respect to soil interaction investigated in the thesis is soil damping, which is not included in the standard method.The standard is to calculate drag force on the riser in the global analysis using the maximum projected diameter of the main tube and auxiliary lines for all wave headings, which results in maximum drag. The wave heading will vary during an operation, and the effect of using the projected diameter for a flow perpendicular to the one giving maximum drag is therefore evaluated. The fluid particle velocities and accelerations used to calculate the forces on the riser are usually found from the undisturbed incoming wave, while they in reality will be affected by disturbance from the MODU. To study this effect, diffraction from a simplified MODU geometry is calculated, and included in the global analysis. In addition, directional data on weather and MODU response is used to get an indication of how significant conservative directional assumptions are for the estimated fatigue damage, as long created waves in the most unfavourable direction usually are applied.The results from the fatigue assessment conclude that the conductor deflections for the studied well are too small for cyclic p-y curves to have an effect on estimated fatigue life. A less stiff wellhead system could get a reduction in fatigue damage, but displacements of that order may not be realistic. The results also show that reduced drag and diffraction from the MODU have relatively little effect on fatigue damage. A reduction in drag force of 23.5 % gives an increase in total fatigue damage of 9 - 10 %. Diffracted wave kinematics result in a reduction in estimated fatigue damage of 8 % for head sea waves, while a 6 % increase in fatigue damage is observed for beam sea waves. Material soil damping is seen to have a significant effect on wellhead fatigue, as the total estimated damage is reduced with 34 - 40 %, with a reduction up to 90 % for certain sea states. There are however great uncertainties associated with the calculated damping values. The results also show that using directional data can give large reductions in estimated wellhead fatigue. The estimated fatigue life of the wellhead is found to be over three times longer for head sea compared to beam sea, and a simplified spreading of the fatigue damage around the circumference of the hotspots is seen to reduce the estimated damage by 25 % in the applied environmental conditions. It can,however, be difficult to justify non-conservative directional assumptions for future operations

Assessment of Uncertainties in Estimated Wellhead Fatigue

During subsea drilling, the motions of the Mobile Offshore Drilling Unit (MODU) and riser cause cyclic bending moments on the wellhead. This may lead to fatigue failure of the component, which can have severe consequences, and there are currently no international standards on how to carry out a wellhead fatigue damage assessment. Through the Joint Industry Project (JIP) Structural Well Integrity, a general wellhead fatigue analysis method has recently been proposed, where the fatigue damage is estimated from a global and a local finite element analysis. There are however several uncertainties regarding the modelling of the systems, which can have significant effects on the estimated fatigue life. In this thesis, some of these uncertainties are identified, and their effect on wellhead fatigue is studied.A short description of a typical subsea drilling system is given, and relevant theory on the topic is presented. The theory consists of an introduction to dynamic response analyses of risers and fatigue life calculations for marine structures, as well as a summary of the general wellhead fatigue analysis method described in the current method.A global riser model is established in Sima/Riflex, which is a software developed for analysis of slender marine structures. A local wellhead system model is also established in the finite element program Abaqus, and the fatigue damage in a typical North Sea well is assessed for a one year long historical operation. The first uncertainty to be studied is the modelling of interaction between conductor and soil. This is usually done using p-y curves, which relate the lateral pressure from the soil to the displacement of the structure. The method describes how to construct p-y curves for both static and cyclic loads, where the static curves are commonly used. In this thesis, the analyses are also conducted with cyclic soil springs. Another modelling aspect with respect to soil interaction investigated in the thesis is soil damping, which is not included in the standard method.The standard is to calculate drag force on the riser in the global analysis using the maximum projected diameter of the main tube and auxiliary lines for all wave headings, which results in maximum drag. The wave heading will vary during an operation, and the effect of using the projected diameter for a flow perpendicular to the one giving maximum drag is therefore evaluated. The fluid particle velocities and accelerations used to calculate the forces on the riser are usually found from the undisturbed incoming wave, while they in reality will be affected by disturbance from the MODU. To study this effect, diffraction from a simplified MODU geometry is calculated, and included in the global analysis. In addition, directional data on weather and MODU response is used to get an indication of how significant conservative directional assumptions are for the estimated fatigue damage, as long created waves in the most unfavourable direction usually are applied.The results from the fatigue assessment conclude that the conductor deflections for the studied well are too small for cyclic p-y curves to have an effect on estimated fatigue life. A less stiff wellhead system could get a reduction in fatigue damage, but displacements of that order may not be realistic. The results also show that reduced drag and diffraction from the MODU have relatively little effect on fatigue damage. A reduction in drag force of 23.5 % gives an increase in total fatigue damage of 9 - 10 %. Diffracted wave kinematics result in a reduction in estimated fatigue damage of 8 % for head sea waves, while a 6 % increase in fatigue damage is observed for beam sea waves. Material soil damping is seen to have a significant effect on wellhead fatigue, as the total estimated damage is reduced with 34 - 40 %, with a reduction up to 90 % for certain sea states. There are however great uncertainties associated with the calculated damping values. The results also show that using directional data can give large reductions in estimated wellhead fatigue. The estimated fatigue life of the wellhead is found to be over three times longer for head sea compared to beam sea, and a simplified spreading of the fatigue damage around the circumference of the hotspots is seen to reduce the estimated damage by 25 % in the applied environmental conditions. It can,however, be difficult to justify non-conservative directional assumptions for future operations

A semi-analytical frequency domain model for efficient design evaluation of spar floating wind turbines

A linear model for efficient design evaluation of spar floating wind turbines is presented, and verified against a nonlinear time domain model with regards to long-term fatigue and short-term extreme response for two different spar designs. The model uses generalized displacements and a semi-analytical approach to establish the equations of motion for the system, which are solved in the frequency domain. The results show agreement within ± 30% for the long-term fatigue considering operational conditions, however, the linear fatigue damage estimates are sensitive to the accuracy of the estimated natural frequency of the first bending mode. The results also suggest that a small number of environmental conditions can be simulated with a nonlinear time domain model to verify and possibly tune the linear model, which then can be used to run the full long-term analysis. Short-term extreme tower base bending moments and surge and pitch motions are observed to be nearly Gaussian above cut-out wind speed, as the response is dominated by wave forces. Consequently, the linear model is able to accurately capture the upcrossing rates, which are used to calculate the characteristic largest extreme response. For an operational case near rated wind speed, the response is somewhat non-Gaussian, which gives larger discrepancies between the linear and nonlinear models. However, due to large mean values in this condition, the total error in the extreme response is reduced, and reasonable agreement is achieved