Wave-Resistance Analysis using FreSCo+ / FRITS
Viscous hydrodynamic flow simulations in the framework of unstructured, interface-capturing, finite-volume methods have matured to an industrial standard by now. Accordingly, the prediction of free-surface flows around floating bodies is a routine application for naval architects. With respect to resistance and propulsion aspects, the steady-state performance in calm-water conditions is usually of particular interest.
Challenge
Although the final solution refers to a steady-state situation, a transient simulation has to be performed. Moreover, the numerical algorithms inhere an explicit time-step (Courant-number) dependency, which drastically enhances the computational effort. Accordingly, some 10000 time-steps are often required to achieve a satisfactory level of force-convergence in conjunction with meshes that typically inhere a couple of million cells. Whilst being of utmost importance to the predictive accuracy of the final solution, the influence of the time step on the stability of a fully implicit approximation seems debatable. Strictly, speaking, the employed time step can be identified as a numerical parameter, which retards the fluid transport within physically admissible bounds.
The FRITS Methodology
FreSCo+ offers a number of CPU-effort reducing techniques for VOF-based simulations of steady wave resistance, which are bundled under the FRITS (Fast RANS Integration To Steady state) approach. The speed-up is primarily due to a sub-cycling approach. The technique adresses the individual time scales of the transported properties which are used to advance the solution with appropriate time steps. The latter facilitates a drastic reduction of the required time to convergence by more than one order of magnitude in wall-clock time. Moreover intialisation of the turbulent flow field based on inviscid solutions and an appropriate adaption of the ship's boundary layer helps to further reduce the computational cost.
Example
The improvements are particularly pronounced for fine-grid computations. The displayed example refers to well known KVLCC2- tanker ship at Fn=0.142 and Re=4.6*10E06, where a vast amount of numerical and experimental data is available. Reported results are obtained on an unstructured mesh with 3,5 Mio. control volumes.
As indicated by the first figure, the predicted wave patterns obtained from FreSCo+ are generally in very good agreemement with experiments (EFD).
As depicted by the longitudinal wave cuts for three different lateral planes, the prediction is in very good agreement with experiments.
Y/Lpp=0.0964
Y/Lpp =0.1581
Y/Lpp=0.2993
In conjunction with the FRITS-technique, force convergence is typically obtained after 2500 iterations. Moreover the FRITS-approach provides a very rapid initial convergence as outlined by the sequence of wave contours given below. The essentials of the flow field are already present after 650 time steps, when conventional techniques are still afflicted by large amounts of artificial initial transients.
