SIMDYN - Time Domain Hydrodynamic Simulation Tool
In the course of my research towards my PhD dissertation, I have developed a time domain simulation program (in FORTRAN) to simulate the nonlinear motions of a vessel at sea. Although the original idea was to create a tool to simulate parametric roll motions of ships, the code has come way far ahead and has taken shape into a generalized time domain hydrodynamic tool. It is a time domain simulation program which can handle the large amplitude of motions of vessel by using an Euler angle formulation and also computes the nonlinear force vector to calculate the nonlinear motions of a vessel in an irregular seas. In particular it includes both nonlinear Froude Krylov and nonlinear hydrostatic forces and moments and also includes a viscous roll damping model for ship shaped structures to help simulate nonlinear phenomena such as parametric roll.
While including the nonlinear Froude Krylov and nonlinear hydrostatics allows modelling strong nonlinear motions, the program is also capable of handling the traditional consistent second order analysis where the second order drift forces and moments are included to evaluate the performance of the mooring system. A mooring model based on the catenary equation is also included to allow for the analysis of moored offshore platforms.
A newer version of the SIMDYN is currently being developed as a Python web application. Click here for more information on the web application.
Salient Features of SIMDYN
Large amplitudes of rotation considered using Euler angle formulation
Solves exact nonlinear equations of motion
Nonlinear Froude Krylov forces and moments
Nonlinear hydrostatic forces and moments
Viscous roll damping model to predict linear and quadratic roll damping
Allows analysis in both zero and forward speed
Pressure history output for mapping into structural analysis programs
Nonlinear Pressure Mapping
In the latest version of the time domain simulation tool SIMDYN capability has been provided to output the pressure time histories which can then be mapped to a structural analysis grid to perform strength analysis. The video below shows the nonlinear pressure time history on KCS container ship in oblique waves. Note that the inclusion of nonlinear Froude Krylov and hydrostatic pressure helps estimate pressure history up to relative waterline instead of the mean waterline.
Parametric response is an instability which results in large responses even when the excitation is close to zero. This nonlinear phenomenon is primarily caused by the time variation of a system parameter such as stiffness (in waves) or inertia.
Parametric Roll Motion of APL China Container Ship
Typically, for a long time parametric roll motion was believed to be a problem for fishing vessels in following waves. However, in the recent years it has come to light that even fast container ships (which have a slender form to achieve higher operational speeds) are highly susceptible to parametric roll in head seas. This instability manifests when the incident regular wave has an encounter frequency which is twice the roll natural frequency. The video below demonstrates this instability of C11 (modified APL China hull form) simulated using SIMDYN (Numerical simulation tool described in detail below).
Moideen, H., Somayajula, A., & Falzarano, J. M. (2013). Parametric Roll of High Speed Ships in Regular Waves. In Proceedings of ASME 2013 32nd International Conferences on Ocean, Offshore and Arctic Engineering (Vol. 5, p. V005T06A095). ASME.
Somayajula, A., & Falzarano, J. M. (2014). Non-linear Dynamics of Parametric Roll of Container Ship in Irregular Seas. In Proceedings of ASME 2014 33rd International Conferences on Ocean, Offshore and Arctic Engineering (pp. 1–10). San Francisco.
Somayajula, A., Guha, A., Falzarano, J., Chun, H.-H., & Jung, K. H. (2014). Added resistance and parametric roll prediction as a design criteria for energy efficient ships. International Journal of Ocean Systems Engineering, 4(2), 117–136.
Somayajula, A., & Falzarano, J. M. (2015). Validation of Volterra Series Approach for Modelling Parametric Rolling of Ships. In Proceedings of ASME 2015 34th International Conferences on Ocean, Offshore and Arctic Engineering. St. John’s, NL, Canada: American Society of Mechanical Engineers.
Parametric Excitation of Single Column Floater
In spar type of platforms, when the damping is low, a coupled instability in the heave and pitch modes is observed when the difference frequency between heave natural period and the incident wave period matches with the pitch natural frequency. This effect has been extensively studied for the classical spar. However, even some of the other designs such as the Single Column Floater are found to be susceptible to this instability. The video below demonstrates the instability of Single Column Floater simulated using SIMDYN.