Planing hull CFD still remains something of a rarity in the simulation world – we have spent some time optimising our workflow to achieve fast results in this demanding field.
Achieving Faster Convergence of Planing Hull CFD Simulations
There are two basic hull types in widespread use. Everyone is familiar with displacement hull ships. While capable of efficiently carrying a great mass of cargo, they are characteristically limited to a slow speed and high drag as they go faster.
The other type of hull is the planing hull, designed to raise the boat out of the water as speed increases and ride on the surface. In doing this, they take advantage of a reduction in drag by skimming across the surface to travel at high speed with less power than an equivalent displacement hull type.
Of course, you don’t get something for nothing and typically the major thing that suffers is the ride comfort.
Therefore, more and more ship designers will turn to CFD as a tool to find the best hull forms that allow the boat to partially rise out of the water at a lower speed and achieve a smoother ride.
These simulations are complex and can take a great deal of time. Using a good guess of the final attitude of the boat as the initial starting condition will achieve a much faster convergence compared to naively setting an initial neutral trim position of the craft.
One method of calculating this final attitude is to apply the Savitsky method to pre-calculate a close approximation of the hull's final planing state based on some straightforward parameters.
Planing Hull CFD with the Savitsky Method
Savitsky developed his method of predicting the attitude of fast planing hulls in 1964, introducing a mathematical approach for predicting the trim angle and draft based on pressure and friction resistance [1].
His method can predict the final attitude of a planing hull craft based on a specified velocity and knowing the hull’s mass, deadrise and location of center of gravity.
This prediction allows a CFD solver to start with an attitude close to the final one, so residual convergence is faster than starting from a neutral attitude state.
Test Case
To test this, I decided to make a comparison between the Savitsky prediction and neutral starting attitude in OpenFOAM. I ran two cases of a simple hull shape (Thornhill et al [2]) with a simplified mesh coarse mesh, one with a neutral initial attitude and the second with the attitude predicted by Savitsky’s method.
In the first case, the hull has been orientated in the horizontal plane with no trim, as if the boat were static on the water and accelerating to the planing speed. In the second analysis, the hull has been rotated according to the calculated trim value obtained from the Savitsky method as though the boat was already travelling at speed on the plane. The initial trim value calculated for this geometry was approximately 7.5°.
Results
I dumped the output log of the convergence history into Excel to create a graph of the hull pitch against the iteration number. It is plain to see that the naive initial guess took much longer to reach the same attitude as the pre-calculated Savitsky attitude case.
We can clearly see that an appropriate initial guess on the trim angle will generate a lot faster convergence on these simulations. The difference in this coarse test case was stark - the Savitsky-conditioned case achieved virtually instant convergence, showing a massive reduction in the simulation time to reach the Savitsky value.
The naive attitude case over-shot the steady convergence of the Savitsky case, taking even longer to achieve a steady state.
Taking into account that this was a test case with a very low resolution mesh size, it is easy to see how this method can achieve big time savings in live cases with much finer mesh resolution.
- Savitsky D. Hydrodynamic design of planing hulls. Vol. 1, Marine Technology. 1964. p. 71–94.
- Thornhill E, Oldford D, Bose N, Veitch B, Liu P. Planing Hull Model Tests for CFD Validation. 6th Can Mar Hydromechanics Struct Conf. 2001;1–10.
