Robert F. Beck

TIME-DOMAIN COMPUTATIONS FOR FLOATING BODIES

Abstract A review of the research carried out at the University of Michigan and elsewhere on the use of time-domain panel methods to compute the hydrodynamic forces acting on floating bodies is presented. Both linear and fully nonlinear computational techniques are presented. The linear problem is solved using a time-domain Green function approach. The fully nonlinear computations are done using an Euler-Lagrange method. At each time step the resulting mixed boundary value problem is solved using a desingularized isolated source. Results are presented for simplified bodies.

Transom-stern Flow for High-speed Craft

Abstract Two series of experiments have been conducted, one at the University of Michigan (U-M), and one by The University of New South Wales (UNSW), with a focus to characterize the flow in the transom region of a high-speed vessel. At U-M, we have tested a destroyer type model, with and without a stern flap, while measuring pressures in the aft region of the hull and on the flap. The model was tested in both the free-to-sinkand-trim condition and the fixed condition. At UNSW, a series of geosimilar models was tested while measuring the free-surface elevation behind the vessel. The non-dimensional free-surface elevation was found to be primarily a function of the calm-water-transom-draft Froude number. To this end, an empirical formula that estimates the unwetting of the transom has been developed. This formula can be employed in a resistance prediction computer program which will provide an accurate calculation of the hydrostatic force on the transom. As a consequence, the total resistance of the vessel can now be computed accurately, even in the low-Froude-number region.

A multipole accelerated desingularized method for computing nonlinear wave forces on bodies

Nonlinear wave forces on offshore structures are investigated. The fluid motion is computed using an Euler-Lagrange time domain approach. Nonlinear free surface boundary conditions are stepped forward in time using an accurate and stable integration technique. The field equation with mixed boundary conditions that result at each time step are solved at N nodes using a desingularized boundary integral method with multipole acceleration. Multipole accelerated solutions require O(N) computational effort and computer storage while conventional solvers require O(N{sup 2}) effort and storage for an iterative solution and O(N{sup 3}) effort for direct inversion of the influence matrix. These methods are applied to the three dimensional problem of wave diffraction by a vertical cylinder.

Three-Dimensional Large Amplitude Body Motions in Waves

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact wetted body surface, the boundary integral equations are numerically solved at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous wetted body geometry. The desingularized method applied on the free surface produces nonsingular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant-strength flat panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceeded until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared to the experiments for both linear computations and body-exact computations.

Time-domain analysis of wave exciting forces on floating bodies at zero forward speed

The problem of determining the exciting forces acting on a rigid floating body due to uni-directional waves has been extensively studied. The problem is usually formulated in the frequency domain by assuming that the incident waves are sinusoidal and of fixed frequency. Results for more general wave systems may then be found using superposition and Fourier analysis. In this paper the problem will be formulated in the time domain. Numerical techniques are developed for bodies of arbitrary shape. The solutions in the time domain and frequency domain are related through the use of Fourier transforms.

Nonlinear Ship Motions in the Time-Domain Using a Body-Exact Strip Theory

Modern offshore structure and ship design requires an understanding of responses in large seas. A nonlinear time-domain method may be used to perform computational analyses of these events. To be useful in preliminary design, the method must be computationally efficient and accurate. This paper presents a body-exact strip theory approach to compute wave-body interactions for large amplitude ship motions. The exact body boundary conditions and linearized free surface boundary conditions are used. At each time step, the body surface and free surface are regrided due to the changing wetted body geometry. Numerical and real hull forms are used in the computations. Validation and comparisons of hydrodynamic forces are presented. Selected results are shown illustrating the robustness and capabilities of the body-exact strip theory. Finally, an equation of motion solver is implemented to predict the motions of the vessel in a seaway.© 2008 ASME

A Real-Time System for Forecasting Extreme Waves and Vessel Motions

The University of Michigan is leading a team that includes subcontractors Ohio State University, Aquaveo, LLC, and Woods Hole Oceanographic Institute to design, implement, and test an Environmental and Ship Motion Forecasting (ESMF) system. The system has application to many challenges associated with offshore operations, including skin-to-skin transfer of cargo/personnel and extreme wave/response prediction. Briefly, the system uses a modified commercial-off-the-shelf (COTS) Doppler marine radar to determine the wave field surrounding the vessel; nonlinear wave theory to propagate the wave surface forward in time; and seakeeping theory to predict future vessel motions. A major challenge is that all computations must be done in real time. This paper will briefly describe the system and show an example application of predicting extreme waves and motions for a floating offshore type platform.Copyright

Nonlinear Ship Motion Computations Using a Time-Domain Body-Exact Slender-Body Approach

This paper continues the development of a computationally efficient potential flow code using a time-domain body-exact strip theory approach. The exact body boundary conditions and linearized free surface conditions are used. Present results include further improvements, validations, and comparisons. Two different formulations to obtain the forces on the vessel are studied: pressure and momentum. Panel distribution techniques, critical for large amplitude motions, are discussed. The slender-body assumption requires finding the longitudinal interaction between sections to compute the hydrodynamic forces. Finally, an equation of motion solver is implemented to predict the six degree-of-freedom motions of the vessel in regular waves, including nonlinear effects.Copyright

Real-time estimation of ocean wave fields from marine radar data

This paper discusses methods for using measurements of the backscattered power and the Doppler shift of radar signals scattered from the ocean surface to compute maps of phase resolved ocean wave fields. Results are compared with buoy and lidar measurements of ocean surface waves off the coast of southern California.

Desingularized Boundary Integral Methods With Application in Wave Hydrodynamics

Desingularized boundary integral equation methods (DBIEM) and their applications in water wave dynamics and body motion dynamics over the past 30 years are reviewed. In solving the potential flow problem for wave dynamics, unlike conventional boundary integral methods, a DBIEM separates the integration surface and the control (collocation) surface, resulting in a BIE with non-singular kernels. The desingularization allows simpler and faster numerical evaluation of the boundary integrals, and thus a fast numerical solution. The paper reviews the fundamental aspects and advantages of DBIEMs. Examples of applications of DBIEMs in wave dynamics and body motion dynamics are given and the outlook of future DBIEMs development is discussed.Copyright