Elsevier

Computers & Fluids

Volume 36, Issue 9, November 2007, Pages 1415-1433
Computers & Fluids

Ship motions using single-phase level set with dynamic overset grids

https://doi.org/10.1016/j.compfluid.2007.01.007Get rights and content

Abstract

The problem of surface ships free to pitch and heave in regular head waves is analyzed numerically with an unsteady Reynolds averaged Navier Stokes (URANS) approach. The unsteady single-phase level set method previously developed by the authors was extended to include six degrees of freedom (6DOF) motions. The method uses rigid overset grids that move with relative motion during the computation, and the interpolation coefficients between the grids are recomputed dynamically every time the grids move. The motions in each time step are integrated implicitly using a predictor–corrector approach. An earth-based reference system is used for the solution of the fluid flow, while a ship-based reference system is used to compute the rigid-body equations of motion. Predicted results for sinkage and trim and resistance at two Froude numbers (medium, Fr = 0.28 and large, Fr = 0.41) were compared against experimental data, showing good agreement. Pitch and heave motions were computed for near-resonant cases at Fr = 0.28 and 0.41, with regular linear head waves with slope ak = 0.025 and wavelength λ = 1.5L, with L the ship length. The predicted motions compare favorably with existing experimental data. A solution for a large amplitude head wave case (ak = 0.075) was also obtained, in which the transom wave breaks and extreme motions are observed. The medium Froude number case was subject to a verification and validation analysis. A problem with two ships pitching and heaving one behind the other is demonstrated.

Introduction

The prediction of ship motions is of importance for all main areas of ship hydrodynamics. Resistance and powering characteristics require the simultaneous computation of the sinkage and trim of the ship. Seakeeping and ship response in a seaway require six degrees of freedom capabilities. The same can be said for maneuvers, in which case some degrees of freedom may be imposed and others predicted. This has been recognized early by designers and researchers, and a variety of computational tools are available to compute loads and responses in waves. However, as the 2005 Seakeeping Committee of the International Towing Tank Conference [1] states in the Final Report and Recommendations, “seakeeping computations are still far from a state of mature engineering science”. Most of the computational tools available today for ship motions are based on potential flow solvers [2], but there have been a few successful efforts in solving viscous ship hydrodynamics with motions. Most of these methods suffer from limitations restricting the applications to small amplitude motions.

Wilson et al. [3] computed the roll damping problem for the surface combatant DTMB 5512 with bilge keels, using a surface tracking technique. The comparison with experiments shows very good agreement, but the motions were restricted to a small amplitude of 10° since the grid fitting process failed at larger amplitudes. Surface capture techniques do not have this limitation since the free surface location is an iso-surface of a three dimensional function, which can take any arbitrary topology. Typical methods using this approach are the density function methods, the volume of fluid (VOF) method, and the level set method. Hochbaum and Vogt [4] used a two-phase level set method to compute the free surface flow around ships in incident waves. The method solved the URANS equations in the non-inertial frame of the ship, limiting the approach to a single moving object. Several applications were shown, and though the validation against experimental data was limited, the comparisons shown are good. Klemt et al. [5] and Klemt [6] used a VOF method to compute the free surface by means of the commercial code Comet. 6DOF motions were added and overset grids were used to allow large amplitude motions. Sato et al. [7] used a density function method and a ship-based coordinate system to compute ship motions in regular head waves. Later, Orihara and Miyata [8], [9] presented a surface capturing method-based on a density function and overset grid capability. With their method, Orihara and Miyata can handle 6DOF ship motions in regular or irregular arbitrary heading waves.

Some CFD studies of pitch and heave of ships in waves are presented in the literature. Hochbaum and Vogt [4] performed computations for a C-Box container ship free to surge, heave and pitch in regular head waves. The comparisons with experimental data show good agreement for small amplitude motions. Weymouth et al. [10] studied the pitch and heave problem for a Wigley hull in head waves using a surface tracking method. Comparisons with experiments for a wide range of wavelengths and Froude numbers also showed good agreement. Again, since a surface tracking method was used the motions were limited to small amplitudes to avoid excessive deformation of the grids that cause the numerical method to fail. Sato et al. [7] computed the Wigley hull and the Series 60 model using their surface capturing technique. Orihara and Miyata [8], [9] computed pitch and heave motions for a container ship in head waves, and compared with experimental results. Emphasis was in predicting the motions transfer functions and the added mass. Though relatively coarse grids were used for all computations, their CFD results are very promising.

In this paper we present computations of pitch and heave of a surface combatant using a single-phase level set method to compute the free surface flow [11], [12], [13]. Large amplitude motions are handled by using dynamic overset grids, with interpolation coefficients obtained at each time step and non-linear iteration during the computation from the Suggar code [14]. The motions are treated independently for several objects by using a common inertial coordinate system and a non-inertial system attached to each ship. Arbitrary heading regular and irregular waves can be handled and are introduced as boundary conditions. This approach allows for the computation of large amplitude motions and interactions between ships.

Pitch and heave computations in regular head waves were performed for two Froude numbers (medium Fr = 0.28 and high Fr = 0.41) and for two wave amplitudes (ak = 0.025 and ak = 0.075). The large amplitude case causes significant motions and exhibits a breaking transom wave, showing a strong damping of the transfer functions with respect to the smaller amplitude wave. The small amplitude, medium Froude number case was subject to a verification and validation (V&V) study by running three grids with refinement ratio 2. Resistance, sinkage and trim are also computed for the two Froude numbers, and the former used to evaluate added resistance. The interaction between two surface combatants one following the other, free to pitch and heave while advancing at Fr = 0.41 in regular waves is also demonstrated.

Section snippets

Mathematical and numerical model

The mathematical and numerical models used in this paper for transient free surface problems have been discussed in detail in [11], and applied, verified and validated for transient ship flows [12] and steady-state problems [13]. The reader is referred to those papers and their references for details on the mathematical and numerical approaches used to solve the fluid flow equations, as only a brief introduction is given in this paper. The solution of the rigid-body equations and the

Computational results

The geometry under consideration is the US David Taylor Model Basin (DTMB) 5512 (L = 3.048 m), a 1:46.6 scale model of a Navy surface combatant in bare hull configuration. This geometry has been one of the benchmarks on the ship hydrodynamics community, selected for validation at the Ship Hydrodynamics CFD Workshops in Gothenburg 2000 [19] and Tokyo 2005 [20]. Experimental data for this geometry has been taken at IIHR (Iowa) and at DTMB and INSEAN (Italy) for the larger model DTMB 5415 (L = 5.72 m).

Conclusions

An extension of the single-phase level set method presented in Carrica et al. [11] to treat object motions has been presented. The method uses an inertial system to solve the fluid flow equations and a ship system to solve the 6DOF equations of motion of different rigid bodies. A dynamic overset grid methodology is used to move the objects arbitrarily within background orthogonal grids.

The method was applied to three problems. First, the steady-state sinkage and trim of a ship advancing in calm

Acknowledgements

This research was sponsored by the Office of Naval Research under Grant N00014-01-1-0073, with Dr. Patrick Purtell as the program manager. The computations were performed at DoD High Performance Computing Modernization Program ARSC and NAVO computing centers. Ralph Noack’s contribution to this research was made possible through support provided by the Department of Defense (DOD) High Performance Computing Modernization Program (HPCMP) Programming Environment and Training (PET) activities

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    1

    Present address: University of Tennessee SimCenter at Chattanooga, Chattanooga, TN 37403, United States.

    2

    Present address: Applied Research Laboratory, The Pennsylvania State University, State College, PA 16804, United States.

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