Bo Terp Paulsen

Static, Dynamic, and Thermal Properties of Compressible Fluid Film Journal Bearings

Modern turbo-machinery applications, high-speed machine tools, and laboratory equipment require ever-growing rotational speeds and high degree of precision and reliability. Gas journal bearings are often employed because they meet the demands of high-speed performance, in a clean environment, and work great efficiency. A great deal of literature has concentrated on the analysis and prediction of the static and dynamic performance of gas bearings, assuming isothermal conditions. The present contribution presents a detailed mathematical modeling for nonisothermal lubrication of a compressible fluid film journal bearing, in order to identify when this type of analysis should be of concern. Load capacity, stiffness, and damping coefficients are determined by the solution of the standard Reynolds equation coupled to the energy equation. Numerical investigations show how bearing geometry, rotational speed and load influence the bearing performance. Comparisons between isothermal and thermohydrodynamic models and discrepancies are quantified for three different types of bearing geometries.

Steep wave loads from irregular waves on an offshore wind turbine foundation: Computation and experiment

Bo Terp PaulsenDTU Mechanical EngineeringDK-2800 Kgs. LyngbyDenmarkEmail: botp@dtu.dkHenrik BredmoseDTU Wind EnergyDK-2800 Kgs. LyngbyDenmarkEmail: hbre@dtu.dkHarry B. BinghamDTU Mechanical EngineeringDK-2800 Kgs. LyngbyDenmarkEmail: hbb@dtu.dkSigne SchloerDTU Wind EnergyDK-2800 Kgs. LyngbyDenmarkEmail: sigs@dtu.dkABSTRACTTwo-dimensional irregular waves on a sloping bed and theirimpact on a bottom mounted circular cylinder is modeled bythree different numerical methods and the results are validatedagainst laboratory experiments. We here consider the perfor-mance of a linear-, a fully nonlinear potential flow solver and afully nonlinear Navier-Stokes/VOF solver. The validation is car-ried out in terms of both the free surface elevation and the inlineforce. Special attention is paid to the ultimate load in case of asingle wave event and the general ability of the numerical modelsto capture the higher harmonic forcing. The test case is repre-sentative for monopile foundations at intermediate water depths.The potential flow computations are carried out in a two-dimensional vertical plane and the inline force on the cylinderis evaluated by the Morison equation. The Navier-Stokes/VOFcomputations are carried out in three-dimensions and the forceis obtained by spatial pressure integration over the wettet areaof the cylinder. In terms of both the free surface elevation andthe inline force, the linear potential flow model is shown to be oflimited accuracy and large deviations are generally seen whencompared to the experimental measurements. The fully nonlin-ear Navier-Stokes/VOF computations are accurately predictingboth the free surface elevation and the inline force. However, thecomputational cost is high relative to the potential flow solvers.Despite the fact that the nonlinear potential flow model is car-ried out in two-dimensions it is shown to perform just as goodas the three-dimensional Navier-Stokes/VOF solver. This is ob-served for both the free surface elevation and the inline force,where both the ultimate load and the higher harmonic forces areaccurately predicted. This shows that for moderately steep irreg-ular waves a Morison equation combined with a fully nonlineartwo-dimensional potential flow solver can be a good approxima-tion.1 IntroductionFor most offshore engineering cases an accurate determina-tion of hydrodynamic loads is crucial for an economic yet safedesign. Traditionally these loads are estimated from laboratoryexperiments and/or numerical computations. Laboratory experi-ments are often costly and normally restricted to small scale dueto the limited size of the test facilities. In the numerical com-putations one is not restricted by the size of the experimental1 Copyright

Application of CFD based wave loads in aeroelastic calculations

Application of CFD based wave loads in aeroelastic calculations Two fully nonlinear irregular wave realizations with different significant wave heights are considered. The wave realizations are both calculated in the potential flow solver Ocean-Wave3D and in a coupled domain decomposed potential-flow CFD solver. The surface elevations of the calculated wave realizations compare well with corresponding surface elevations from laboratory experiments. In aeroelastic calculations of an offshore wind turbine on a monopile foundation the hydrodynamic loads due to the potential flow solver and Morison’s equation and the hydrodynamic loads calculated by the coupled domain decomposed potentialflow CFD solver result in different dynamic forces in the tower and monopile, despite that the static forces on a fixed monopile are similar. The changes are due to differences in the force profiles and wave steepness in the two solvers. The results indicate that an accurate description of the wave loads is very important in aeroelastic calculations especially in cases where the aerodynamic loads and damping are insignificant.

Higher-Harmonic Response of a Slender Cantilever Beam to Fully Nonlinear Regular Wave Forcing

The higher-harmonic response of a vertical cantilever beam to fully nonlinear wave loads is investigated. Such responses are also known as ‘ringing’ and is of practical interest in the context of offshore wind turbine foundations which, in contrast to the classical incidents of ringing at deep water, are placed at intermediate or shallow water.The purpose of the study is to provide generic results which can be of later use for the interpretation of more complex cases of irregular wave forcing. To this end, the problem parameters are defined and reduced by dimensional analysis. A simple numerical model is proposed, based on linear beam theory and fully nonlinear regular stream function waves. The hydrodynamic forces are determined from the extended Morison equation.Parametric studies of the response dependence to relative forcing period, wave height and depth are presented and discussed. A central finding of the paper is that for waves of 85% maximum height, the third-harmonic response increases substantially when the depth is reduced from deep-water conditions into intermediate depth.Copyright

WAVE IMPACT LOADS ON OFFSHORE GRAVITY BASED STRUCTURE

Aibel is developing an offshore power converter platform concept. Its foundation is gravity-based and consists of four columns interconnected by a ring-shaped pontoon at the seabed. The platform is intended for water depths in the order of 20 to 40m. In these waters, breaking waves typically cause large wave loads on the foundation that need to be accounted for in the design. The slamming loads, pressures and air gap at the platform were investigated with a combined approach of physical and numerical modeling. This paper summarizes the set-up, test program, measurement techniques, results and analysis of the physical model tests.The tests showed that reflection and diffraction patterns caused a significant steepening of the waves between the columns, reducing the air gap and increasing the slamming frequency and magnitude on the downstream columns and underside of the deck. Excitation of resonant wave modes was identified for certain wave frequencies. Although the global wave loads were primarily governed by inertia, largest loads occurred under slamming impacts on the upstream columns, in phase with the inertial force.Copyright