MODELLING THE HEAVE OSCILLATIONS OF VERTICAL CYLINDERS WITH DAMPING PLATES

The laminar flow around heaving axisymmetric and three-dimensional cylinders with damping plates is numerically studied for various Keulegan-Carpenter numbers. The Navier-Stokes equations are solved using OpenFOAM, which is applied to the flow on a moving mesh. For processing of results the semi-empirical Morison equation is used. Calculations are conducted for one cylinder, one cylinder with one disk, one cylinder with two disks, and one cylinder with one pentagonal plate. The calculated values are compared against experimental data.

Effect of Air Fraction on Force Coefficients in Oscillatory Flow

The forces on marine and offshore structures are often affected by spilling breakers. The spilling breaker is characterized by a roller of mixed air and water with a forward speed approximately equal to the wave celerity. This high speed in the top of the wave has the potential to induce high wave loads on upper parts of the structures. This study analyzed the effect of the air content on the forces. The analyses used the Morison equation to examine the effect of the percentage of air on the forces. An experimental set-up was developed to include the injection of air into an otherwise calm water body. The air-injection did introduce a high level a turbulence. It was possible to assess the amount of air content in the water for different amounts of air-injection. In the mixture of air and water the force on an oscillating square cylinder was measured for different levels of air-content, — also in the case without air. The measurements indicated that force coefficients for clear water could be use in the Morison equation as long as the density for water was replaced by the density for the mixture of air and water.

Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads

This paper is devoted to the random vibration analysis of jacket platforms under wave loads using the explicit time-domain approach. The Morison equation is first used to obtain the nonlinear random wave loads, which are discretized into random loading vectors at a series of time instants. The Newmark-β integration scheme is then employed to construct the explicit expressions for dynamic responses of jacket platforms in terms of the random vectors at different time instants. On this basis, Monte Carlo simulation can further be conducted at high efficiency, which not only provides the statistical moments of the random responses, but also gives the mean peak values of responses. Compared with the traditional power spectrum method, nonlinear wave loads can be readily taken into consideration in the present approach rather than using the equivalent linearized Morison equation. Compared with the traditional Monte Carlo simulation, the response statistics can be obtained through the direct use of the explicit expressions of dynamic responses rather than repeatedly solving the equation of motion. An engineering example is analyzed to illustrate the accuracy and efficiency of the present approach.

Assessment of LNG Pump Tower Loads

The assessment of design loads acting on Liquefied Natural Gas (LNG) pump tower are widely based on Morison equation. However, the Morison equation lacks consideration of transverse flow, impact loads and the interaction between fluid and structure. Studies dealing with a direct simulation of LNG pump tower loads by means of Computational Fluid Dynamics (CFD), which can cover the aforementioned effects, are currently not available. A comparative numerical study on LNG pump tower loads is presented in this paper focusing on the following two questions: Are impact loads relevant for the structural design of LNG pump towers? In which way does the fluid-structure interaction influence the loads? Numerical simulations of the multiphase problem were conducted using field methods. Firstly, Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations, extended by the Volume of Fluid (VoF) approach were used to simulate the flow inside a three-dimensional LNG tank in model scale without tower structure. The results were used to validate the numerical model against model tests. Motion periods and amplitudes were systematically varied. Velocities and accelerations along the positions of the main structural members of the pump tower were extracted and used as input data for load approximations with the Morison equation. Morison equation, URANS and Delayed Detached Eddy Simulation (DDES) computed tower loads were compared. Time histories as well as statistically processed data were used. Global loads acting on the full (with tower structure) and simplified structure (no tower structure, but using Morison equation) are in the same order of magnitude. However, their time evolution is different, especially at peaks, which is considered significant for the structural design.

Experimental Study on the Wave Loads on Monopile and Jacket Type Support of Offshore Wind Turbines

As the offshore fixed wind turbine developed, more ones will be installed in the sea field with the depth 15–50 meters. Wave force will be one of the main forces that dominate the design of the wind turbine base, which is calculated using the Morison equation traditionally. This method can predict the wave forces for the small cylinders if the drag and inertia coefficients are obtained accurately. This paper will give a series scaled tests of monopile and jacket type base of the offshore wind turbine in tank to study the nonlinear wave loads.

Viscous Drift Forces on a Semi-Submersible in Combined Wave and Current

A time domain simulation tool is used to setup a numerical simulation model in which the wave loads of the potential flow are combined with the viscous drag force computed by the Morison equation. The drag coefficients in the Morison equation are determined to provide the best numerical results compared to model test data. The numerical simulations and analytic solutions have been used to examine the characteristics of mean viscous drift force on the semi-submersible for fixed condition. The results show that the mean viscous drift force is mainly produced by the column. The column is divided into splash zone and submerged zone because they give much different mean viscous drift force. In high waves, the splash zone leads to mean drift force much larger than the submerged zone for both wave-only and wave-current coexisting flow fields. The present results clearly show that the drag coefficients can be expressed as a function of the Keulegan-Carpenter number, especially for high waves. There is strong correlation between regular and irregular waves for both wave-only and wave-current coexisting flow fields. If current is present, the drag coefficient decreases significantly.

Application of Morison Equation in Irregular Wave Trains With High Frequency Waves

Most numerical models for the analysis of offshore wind platforms are based on one of two different approaches, depending on how waves forces are applied to the structure: 1) the potential flow theory, and 2) the Morison equation. Potential flow theory allows to compute the wave forces more accurately when diffraction is relevant. Otherwise, this kind of models assume a fixed position of the floating platform when computing the wave forces. Additionally, second-order effects, as the position and the spin of the structure relative to the incident wave can only be taken into account if second order potential flow is considered. On the other hand, Morison equation can apply the wave forces on a structure based on its spin and position which can be assessed at each time step, but is prone to overestimate the waves forces at the frequencies where diffraction is relevant. In this paper, a modification of the implementation of the Morison equation is presented. This modification allows to reduce the forces in the diffraction frequency range based on the real response from MacCamy and Fuchs’s diffraction theory for cylinders. The implementation can be applied using a frequency-dependent coefficient of added mass, or modifying the amplitudes of the incident waves in the diffraction frequency range in a way that the accelerations derived from the regular wave theory used for the Froude-Krylov wave force computation in Morison equation are equivalent to those computed in the diffraction theory. The implementation is tested in the FloawDyn code, developed at the UPC, and FAST from NREL.