An Improved Body-Exact Method to Predict the Maneuvering of Ships in a Seaway

2019 ◽  
Author(s):  
Rahul Subramanian ◽  
Robert F. Beck
Keyword(s):  
Incident Wave ◽  
Body Position ◽  
Surface Boundary ◽  
Wave Surface ◽  
Computationally Efficient ◽  
Regular Waves ◽  
Viscous Effects ◽  
Surface Boundary Conditions ◽  
Strip Theory ◽  
Calm Water

Abstract Over the last decade, the importance of considering the effects of waves on the maneuvering characteristics of ships has been widely recognized. This paper presents the application of a recently developed nonlinear body-exact scheme (Subramanian, Rakesh, and Beck (2018)) to directly simulate the maneuvering characteristics of a container ship in calm water and in regular waves. In the present body-exact scheme, the perturbation free surface boundary conditions are transferred to a representative incident wave surface at each station at each time. The hydrodynamic forces are computed on the exact instantaneous wetted surface formed by the intersection of the incident wave surface with the exact body position at each time. It is proposed that this model will not only improve first order sea loads but also the higher order drift force predictions which are critical for determining the trajectory of a maneuvering vessel in a seaway. The strip theory formulation has been found to be numerically stable, robust and computationally efficient, which are all critical aspects when performing long time maneuvering simulations. The hull maneuvering, rudder and propeller forces are adopted from standard systems-based approaches that are used to predict calm water maneuvers. Care is taken to ensure that ideal fluid effects are separated from viscous effects and not double counted. Results are presented for turning circle maneuvers in calm water and regular waves incident at various headings and wavelengths. The numerical results are compared with available experiments.

An Improved Body-Exact Method to Predict Large Amplitude Ship Roll Responses

2018 ◽  
Author(s):  
Rahul Subramanian ◽  
Naga Venkata Rakesh ◽  
Robert F. Beck
Keyword(s):  
Incident Wave ◽  
Large Amplitude ◽  
Nonlinear Models ◽  
Body Position ◽  
Computational Cost ◽  
Offshore Structures ◽  
The Body ◽  
Surface Boundary ◽  
Strip Theory ◽  
New Formulation

Accurate prediction of the roll response is of significant practical relevance not only for ships but also ship type offshore structures such as FPSOs, FLNGs and FSRUs. This paper presents a new body-exact scheme that is introduced into a nonlinear direct time-domain based strip theory formulation to study the roll response of a vessel subjected to moderately large amplitude incident waves. The free surface boundary conditions are transferred onto a representative incident wave surface at each station. The body boundary condition is satisfied on the instantaneous wetted surface of the body below this surface. This new scheme allows capturing nonlinear higher order fluid loads arising from the radiated and wave diffraction components. The Froude-Krylov and hydrostatic loads are computed on the intersection surface of the exact body position and incident wave field. The key advantage of the methodology is that it improves prediction of nonlinear hydrodynamic loads while keeping the additional computational cost small. Physical model tests have been carried out to validate the computational model. Fairly good agreement is seen. Comparisons of the force components with fully linear and body-nonlinear models help in bringing out the improvements due to the new formulation.

A Nonlinear Mathematical Model for Ship Turning Circle Simulation in Waves

2005 ◽  
Vol 49 (02) ◽  
pp. 69-79 ◽  
Author(s):  
Ming-Chung Fang ◽  
Jhih-Hong Luo ◽  
Ming-Ling Lee
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Regular Waves ◽  
Nonlinear Mathematical Model ◽  
Ship Maneuvering ◽  
Sea Trial ◽  
Six Degrees Of Freedom ◽  
Strip Theory ◽  
Calm Water ◽  
Maneuvering Motion

In the paper, a simplified six degrees of freedom mathematical model encompassing calm water maneuvering and traditional seakeeping theories is developed to simulate the ship turning circle test in regular waves. A coordinate system called the horizontal body axes system is used to present equations of maneuvering motion in waves. All corresponding hydrodynamic forces and coefficients for seakeeping are time varying and calculated by strip theory. For simplification, the added mass and damping coefficients are calculated using the constant draft but vary with encounter frequency. The nonlinear mathematical model developed here is successful in simulating the turning circle of a containership in sea trial conditions and can be extended to make the further simulation for the ship maneuvering under control in waves. Manuscript received at SNAME headquarters February 19, 2003; revised manuscript received January 27, 2004.

Three-Dimensional Large Amplitude Body Motions in Waves

2007 ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Submerged Body ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

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 panels on the exact submerged body surface, the boundary integral equations are solved numerically 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 changing submerged body geometry. The desingularized method applied on the free surface produces non-singular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant strength 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 proceed 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 with the experiments for both linear computations and body-exact computations.

Time-Domain Simulations of Radiation and Diffraction Forces

2010 ◽  
Vol 54 (02) ◽  
pp. 79-94 ◽  
Author(s):  
Xinshu Zhang ◽  
Piotr Bandyk ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
The Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Strip Theory

Large-amplitude, time-domain, wave-body interactions are studied in this paper for problems with forward speed. Both two-dimensional strip theory and three-dimensional computation methods are shown and compared by a number of numerical simulations. 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 body surface, the boundary integral equations are solved numerically at each time step. The strip theory method implements Radial Basis Functions to approximate the longitudinal derivatives of the velocity potential on the body. 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 changing wetted body geometry. Extensive results are presented to validate the efficiency of the present methods. These results include the added mass and damping computations for a Wigley III hull and an S-175 hull with forward speed using both two-dimensional and three-dimensional approaches. Exciting forces acting on a Wigley III hull due to regular head seas are obtained and compared using both the fully three-dimensional method and the two-dimensional strip theory. All the computational results are compared with experiments or other numerical solutions.

The Transient Capsize Diagram—A New Method of Quantifying Stability in Waves

1991 ◽  
Vol 35 (01) ◽  
pp. 58-62 ◽  
Author(s):  
R. C. T. Rainey ◽  
J. M. T. Thompson
Keyword(s):  
Computer Simulation ◽  
Dynamic Systems ◽  
Wave Steepness ◽  
Dynamic Systems Theory ◽  
Regular Waves ◽  
Desktop Computers ◽  
Strip Theory ◽  
Calm Water ◽  
Recent Developments ◽  
The Stability

It is argued that a plot of wave steepness against wave period, showing the combinations which cause capsize, is a well-defined measure of the stability of a ship or ocean vehicle in waves, provided the conditions are transient, that is, the vessel is initially in relatively calm water, and is suddenly hit by a train of regular waves. This conclusion is a consequence of recent developments in dynamic systems theory. Such Transient Capsize Diagrams can obviously be obtained by model testing; it is also argued that they could be obtained by computer simulation on contemporary desktop computers, taking advantage of recent developments in nonlinear strip theory.

A Forward-Speed Body-Exact Strip Theory

2015 ◽  
Author(s):  
Piotr J. Bandyk ◽  
George S. Hazen
Keyword(s):  
High Frequency ◽  
Numerical Data ◽  
The Body ◽  
Surface Boundary ◽  
Forward Speed ◽  
Rankine Source ◽  
High Frequency Oscillations ◽  
Surface Boundary Conditions ◽  
Strip Theory ◽  
Acceleration Potential

This paper develops an extension to the body-exact strip theory of Bandyk, Beck, and Zhang [1–8], focused on improved prediction of forward-speed effects. One of the known limitations of standard strip theory is the treatment of forward speed terms. The free surface boundary conditions completely neglect the forward speed, which is usually justified by the argument of high-frequency oscillations. The pressure equation on the body includes a speed-dependent term that must computed, most commonly using the Ogilvie-Tuck theorem or numerical approximations. The strip theory variation described here circumvents these deficiencies by applying the 2D+T approach. The model assumes that each two-dimensional frame, in which a boundary value problem (BVP) is solved, remains fixed relative to an earth-fixed frame. The numerical model is based on a time-domain Rankine source method, using the same body-exact approximation as described in earlier work [1]. A suitable acceleration potential BVP is derived. Added mass and damping coefficients are calculated for two Wigley hulls, using the the standard body-exact approach and forward-speed 2D + T variant, and compared to existing model test and numerical data.

Some Extensions of the Classical Approach to Strip Theory of Ship Motions, Including the Calculation of Mean Added Forces and Moments

1978 ◽  
Vol 22 (01) ◽  
pp. 1-19 ◽  
Author(s):  
Theodore A. Loukakis ◽  
Paul D. Scfavounos
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Forced Oscillations ◽  
Ship Motions ◽  
Regular Waves ◽  
Strip Theory ◽  
Calm Water ◽  
Exciting Forces ◽  
New Formulation

The application of the dynamical theory to the problem of a ship moving with constant forward speed on a free surface has been extended to include the exciting forces in oblique regular waves. As a result, it has become possible to derive a new formulation for the equations of motion, for a ship moving with five degrees of freedom. The application of the same theory has yielded formulas for the calculation of the mean added resistance and drift force in oblique regular waves and the calculation of all mean forces and moments for the forced oscillations of a ship in calm water.

Three-Dimensional Large Amplitude Body Motions in Waves

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

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.

scholarly journals Numerical Investigation of Wave-Body Interactions in Shallow Water

2014 ◽  
Author(s):  
Yi Luo ◽  
Torgeir Vada ◽  
Marilena Greco
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Numerical Study ◽  
Surface Boundary ◽  
Regular Waves ◽  
Incoming Wave ◽  
Surface Boundary Conditions ◽  
First Case ◽  
Non Linear ◽  
Linear Effects

Present investigation is based on a numerical study using a time-domain Rankine panel method. The effort and novelty is to extend the applicability of the solver to shallower waters and to steeper waves by including additional non-linear effects, but in a way so to limit the increase in computational costs. The challenge is to assess the improvement with respect to the basic formulation and the recovery of linear theory in the limit of small waves. The wave theories included in the program are Airy, Stokes 5th order and Stream function. By their comparison the effect of the incoming-wave non-linearities can be investigated. For the free-surface boundary conditions two alternative formulations are investigated, one by Hui Sun [1] and one developed here. The two formulations combined with the above-mentioned wave theories are applied to two relevant problems. The first case is a fixed vertical cylinder in regular waves, where numerical results are compared with the model tests by Grue & Huseby [2]. The second case is a freely floating model of a LNG carrier (with zero forward speed) in regular waves, where computations are compared with the experimental results from the EC project “Extreme Seas”. This comparison revealed several challenges such as how to interpret/post process the experimental data. Some of these are described in the paper. After careful handling of both computed and measured data the comparisons show reasonable agreement. It is proven that including more non-linear effects in the free-surface boundary conditions can significantly improve the results. The formulation by Hui Sun gives better results compared to the linear condition, but the present formulation is shown to provide a further improvement, which can be explained through the nonlinear terms included/retained in the two approaches.

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