Simulation based calculation of ship motions in extreme seas with a body-exact strip theory approach

For the initial and detail design stages of naval platforms, the fidelity of seakeeping calculations in extreme seas is open to discussion due to the inadequacy of the linear theory of ship motions. Reliability of the ship motion calculations is important for the design and verification of the ship itself and the systems on board. These systems, especially include active roll stabilizer fins, active motion interceptors, rudder roll stabilization, helicopter securing & traversing, helicopter visual landing aid, and all sensors & weapons. In this study, a method has been developed to calculate the ship motions in extreme seas in comparison with experimental results. For this purpose, first the simulation based analysis method of ship motions and wave elevation was discussed with the procedure of spectral verification. These simulations are also known as the real time computer experiments. The DTMB 5415 hull form (in forward motion with the Froude number of 0.41), which is the prelimary form of the DDG-51, is used for this study. The ship motion and wave surface simulation (in short-crested irregular seas) code is developed in a C++ programming language which can be controlled by the user in real time on screen. The visualization is achieved using Object-Oriented Graphics Rendering Engine (OGRE) Software Development Kit. The simulation works real time and has no time limitation (infinite simulation duration). Time step of the "real time simulation" is the time passed since the last frame rendered, i.e. depends on the frame rate. The simulation can be accelerated or decelerated using predefined large or small fixed time steps for analysis purpose. The simulation has also real time controllable parameters for the ship and the environment. The controllable ship parameters are the speed and rudder angle. The controllable environment parameters are the sea area, sea-state and wave direction. In order to determine the ship motions for the simulation, three Cartesian coordinate systems are used. These are the earth-fixed, moving (inertial), and the body-fixed system. The orientation of the body-fixed system relative to the inertial system gives the translational (surge, sway, heave) and rotational (roll, pitch, yaw) motions of the ship. The body-fixed coordinate system moves with all the motions of the ship. All formulations including sea-state, sea-spectra, directional spectrum and derived responses which are required to create such a simulation are given. The time series data for the long or short crested irregular sea surface and the ship responses were generated by the well-known superposition algorithm for the selected sea state and sea area. The time series data for the ship motions were generated from the initially calculated frequency domain RAOs and the corresponding motion spectra. Sea states were defined by the World Meteorological Organization standard sea state code (Douglas Scale). The wave height range of this sea-state code (WMO Code Table 3700) can be regarded as significant wave height range for the naval engineering purpose. Sea areas were described mathematically by the sea spectrum formulas. These are ITTC One-, ITTC Two-Parameter and JONSWAP sea-spectra. The mean values of the significant wave height range can be used to define the sea-state, but the corresponding modal wave periods for each sea-state should be known to define the sea area. The sea spectrum formulas are unidirectional, i.e. can be used for a description of a long crested irregular sea. In order to describe a short crested irregular sea it is required to have a multi−directional spectrum. The time series of the derived responses like absolute motions and accelerations; can also be obtained by the "real time computer experiments". Verification of the time series of wave elevation and all responses, including the derived ones were performed using the spectral analysis technique which includes discrete Fourier transform (DFT), and smoothing algorithms. For the verification, the spectral density functions derived from time series data were compared to the original spectra, which were used for the generation of the time series. For the short crested wave data, the spectral verification were performed separately for each secondary wave direction component. Observation of the deck wetness, slamming or emergence at any location is also feasible from the relative motion time history. So the analysis of the simulation results provides sufficient information about the extreme motions and accelerations. Furthermore, the results of this study may also be suitable for the ship handling simulators or helicopter landing on ship simulations for more realistic visualization. Although not within the scope of this thesis, the simulated time series of ship motions and wave elevation may also be utilized to derive the vertical distortion, shear force and bending moment distribution of ship sections using ship hydroelasticity theory. It is found that this analysis method can be adapted to design and verification studies for both the naval platform itself and the systems on board effectively. Inspired by these studies a simulation based calculation of symmetric ship motions was performed in long crested irregular head seas, in addition with a body-exact strip theory approach. According to strip theory, the added mass and damping coefficients in the equations of motions are given by the integrals over the length of the ship, which contains two dimensional sectional added mass and damping coefficients for heave. The two dimensional sectional added mass and damping coefficients are calculated on the instantaneous hull wetted surface by the Frank Close-Fit method. In order to calculate two dimensional sectional added mass and damping coefficients, the Frank Close-Fit method solves a boundary-value problem of potential theory, assuming incompressible and inviscid, and irrotational flow. The surface tension effects and the nonlinear terms of the free surface condition, the kinematic boundary conditions and the Bernoulli equation are neglected. Along the two dimensional section forced into the simple harmonic motion, the hydrodynamic pressures in phase with the displacement and in phase with the velocity, which yields to sectional added mass and damping coefficients, is obtained from the velocity potential using linearized Bernoulli equation. This velocity potential satisfies, the Laplace equation in the fluid domain, the free surface condition on the free surface, the bottom condition, the kinematic boundary condition and finally, the radiation condition at large distances from the ship's section. The velocity potential can be represented by the integration of the real point-source distribution that have a complex source strength over the immersed contour of the section. Using the kinematic boundary condition the velocity potential can be solved. The time series data is generated for both body-linear and body-exact condition. The time series data for the body linear condition is generated from the initially calculated frequency domain RAOs and the corresponding motion spectra. The body linear time series data is used to for the validation of the spectral analysis. The time series data for the wave surface in moving (inertial) coordinate system is only used for the generation of the time series data for the body-exact condition. The initially calculated linear frequency domain RAOs are used at t = 0. At each time step, the intersection points of the wave and the ship sections are transformed into the body-fixed coordinate system. The strip theory calculation along with the Frank Close-Fit method for each step is updated using the wet part of each section Verification and comparison of the simulated data were achieved using the spectral analysis technique which includes discrete Fourier transform (DFT), and smoothing algorithms. For the verification, the spectral density functions and the corresponding RAOs derived from the "body-linear" and "body-exact" time series data were compared to the calculated spectra and RAOs which were used for the generation of the time series. The results were also compared with the experimental data, and the ANSYS AQWA software results. These simulation results (time series data) also provide satisfactory information about the extreme motions and accelerations. The importance of the simulation based analysis is its practical and innovative nature. The desired length of time series data for any ship response, including the derived ones can be generated without any cost and restrictions except the computer performance. Comparison of the performance of different hull forms in the same irregular sea condition is possible with this simulation technique. If supported by experimental results, a database of the responses from the different type of hull forms can also be generated. Moreover, the real time simulation based analysis method may prevent the over-design issues and allow the refinement of the design criteria for both the naval platform itself and the systems on board. This state-of-the-art method in addition with a "body-exact strip theory approach" ensures the consistent assessment of the seakeeping performance in extreme sea condition. As a result, it is evaluated that this calculation method can be used in the design stages of naval platforms.