Roll Damping of a Twin-Screw Vessel: Comparison of RANSE-CFD with Established Methods

Abstract

A RANSE-CFD method is applied to estimate the roll damping of a modern twin-screw RoPax vessel. The simulations are carried out in full scale and with an undisturbed water surface. The harmonic forced roll motion technique is implemented. The influence of ship speeds, the vertical position of the roll axis and roll amplitudes up to 35${^\circ }$ are investigated. The interaction between the bilge keels and the ship hull is analyzed. The damping effects of further appendages are discussed. All simulation results are compared with the established method developed by Ikeda and a neural network method based on Blume’s roll damping measurements. The established methods were developed based on studying results of single-screw ships. It can be concluded that both established methods provide acceptable results in certain ranges. For large roll amplitudes, the established methods are out of range and cannot deliver reliable results.

Appendix

SIMB$\mathbf {^3}$-method: Blume’s roll damping measurements carried out at the Hamburg Ship Model Basin (HSVA) of various ship hulls of the 1970s and before were summarized as artificial neural network. This was developed by Salas Inzunza, Mesbahi, Brink and Bertram Salas Inzunza et al. (2001) based on the measurement results of Blume: we call it here SIMB$\mathbf {^3}$-method.

For the artificial neural network, a sigmoid function is used:

$$\begin{aligned} sig(x)=\frac{1}{1+e^{-x}}. \end{aligned}$$

(11.15)

The non dimensional roll damping coefficient

$$\begin{aligned} \hat{B}=\sqrt{\zeta ^2\cdot \frac{2g\overline{GM}^2}{B_{WL}^3\omega _0^2} } \end{aligned}$$

(11.16)

depends on the gravity constant g, metacentric height $\overline{GM}$, ship breadth $B_{WL}$, roll resonance frequency $\omega _0$ and the damping ratio $\zeta$:

$$\begin{aligned} \zeta =0.26525\cdot sig[xx_1+xx_2+xx_3+xx_4+xx_5+1.121]-0.071725 \end{aligned}$$

(11.17)

with

$$\begin{aligned} \begin{aligned} xx_1&=-0.15923\cdot sig (-0.54784 - 0.35004x_1 - 0.32394x_2 - 0.49683x_3 - 0.7495x_4)\\ xx_2&=1.8997\cdot sig ( 0.48293 - 2.71914x_1 - 5.87083x_2 + 5.55228x_3 - 0.99526x_4)\\ xx_3&=-0.45902\cdot sig (-0.35086 - 0.3666x_1 - 0.21579x_2 - 0.78014x_3 - 1.1742x_4)\\ xx_4&=-2.0167\cdot sig ( 4.2884 - 4.5154x_1 + 1.4302x_2 - 0.30797x_3 - 3.9884x_4)\\ xx_5&=-2.1800\cdot sig (-0.09468 + 3.1056x_1 - 5.4142x_2 -3.1332x_3 +1.7851x_4) \end{aligned} \end{aligned}$$

and

$x_1=0.16807\cdot (B_{WL}/d) -0.12017$

$x_2=1.23456\cdot C_B - 0.28765$

$x_3=1.33333\cdot Fr +0.3$

$x_4=0.026667\cdot \varphi _a + 0.166667$.

To achieve the roll resonance frequency $\omega _0=0.435\; [\mathrm{rad/s}]$ of the RoPax vessel, a metacentric height of $\overline{GM}=2.09\,[\mathrm{m}]$ is selected. The roll radius of gyration of the virtual and ship mass is assumed to be $i_\Phi =0.4\cdot B_{WL}\;[\mathrm{m}]$.