Author | Starke, A.R. |

Title | The prediction of scale effects on ship wave systems using a steady iterative RANS method |

Conference/Journal | NUTTS 2004 Symposium, Hamburg |

Month | October |

Year | 2004 |

Abstract

Model testing of ships is usually performed at equivalent Froude numbers to obtain equal wave patterns at model scale and at full scale. However, once the Froude number is fixed, one can not also obtain equivalent Reynolds numbers. Typically, in ship design projects the Reynolds number at model scale is a factor one hundred smaller than at full scale. To account for the so-called scale effects caused by the difference in Reynolds number, extrapolation procedures are used. The primary scale effect on the flow is a decrease of the boundary-layer thickness on the hull and a corresponding decrease of the width of the wake behind the stern with increasing Reynolds number. This results in a considerable change of the velocity distribution in the propeller plane. A secondary, and therefore less pronounced, scale

effect is caused by the interaction between the viscous flow and the wave pattern. Wave effects on the viscous flow around the hull may be significant for all cases with substantial wave making, as the wavy surface affects the development of the boundary layer all along the

hull. On the other hand, viscous effects on the wave pattern are generally insignificant and only substantial in the stern region, as is confirmed by many validations of non-linear panel methods. Viscous effects are expected to result in a reduction of the height of the stern wave system and an upstream shift of the first wave crest behind the stern. The level of this reduction depends on the amount to which the flow itself is affected by viscosity. Since the width of the boundary layer and the wake decrease with increasing Reynolds number, so does the reduction of the stern wave system. This secondary scale effect on the wave system is not specifically accounted for in extrapolation procedures. However, with the development of solution methods for the free-surface viscous-flow problem, it has now become possible to calculate these effects, which is the subject of this paper. Results will be presented for a full-block tanker, sailing at a relatively low Froude number. Attention will be given to the grid dependency of the solution and the results will be validated against available experiments.

Model testing of ships is usually performed at equivalent Froude numbers to obtain equal wave patterns at model scale and at full scale. However, once the Froude number is fixed, one can not also obtain equivalent Reynolds numbers. Typically, in ship design projects the Reynolds number at model scale is a factor one hundred smaller than at full scale. To account for the so-called scale effects caused by the difference in Reynolds number, extrapolation procedures are used. The primary scale effect on the flow is a decrease of the boundary-layer thickness on the hull and a corresponding decrease of the width of the wake behind the stern with increasing Reynolds number. This results in a considerable change of the velocity distribution in the propeller plane. A secondary, and therefore less pronounced, scale

effect is caused by the interaction between the viscous flow and the wave pattern. Wave effects on the viscous flow around the hull may be significant for all cases with substantial wave making, as the wavy surface affects the development of the boundary layer all along the

hull. On the other hand, viscous effects on the wave pattern are generally insignificant and only substantial in the stern region, as is confirmed by many validations of non-linear panel methods. Viscous effects are expected to result in a reduction of the height of the stern wave system and an upstream shift of the first wave crest behind the stern. The level of this reduction depends on the amount to which the flow itself is affected by viscosity. Since the width of the boundary layer and the wake decrease with increasing Reynolds number, so does the reduction of the stern wave system. This secondary scale effect on the wave system is not specifically accounted for in extrapolation procedures. However, with the development of solution methods for the free-surface viscous-flow problem, it has now become possible to calculate these effects, which is the subject of this paper. Results will be presented for a full-block tanker, sailing at a relatively low Froude number. Attention will be given to the grid dependency of the solution and the results will be validated against available experiments.