|Title: Calculation of Penetrated Wake Alignments in a Three Dimensional Panel Method for the Rudder Design Process|
|Written by: Arne Falkenhorst, Christoph M. Steinbach|
|in: 5th Symposium on Marine Propulsors, Espoo, Finland 2017|
Abstract: For the classic design approach of lifting surfaces in naval architecture each device (e.g. propellers, rudders or stabilizers) is treated as a standalone design problem. The panel codes that are often applied to this design purpose use a steady approach and a simplified wake treatment. This procedure is triggered by the project structure of manufacture with a need for short project lead times and furthermore the simplification leads to an improved numerical stability. Especially the calculation of vortex induced velocities in or close to the vortex core leads to singularities in case of standard vortex models. This is not an issue, as long as only one device is considered. Especially to improve the design process of rudders to a higher accuracy it is required to calculate the rudder in the propeller slipstream for typical propeller-rudder arrangements. Another industrial problem, primarily in inland shipping, is the interaction between two rudders in one propeller slipstream, and hence the interaction between two rudder wakes. These problems can be separated into the interaction between a wake and another body and the interaction of two wakes. This paper discusses a method to calculate the interaction of vortex wakes. The approach will be later used in the above described design purpose. A steady 3D BEM–panel methods including a Kutta - condition for lift generation is utilized for the calculation. The paper concentrates on two important features implemented to improve the behaviour of the wake. The first is the force free wake alignment. This will give later the ability, to take the effect of the (average) non-uniform inflow from the propeller into account. The result is a moveable and subdivided wake, as for unsteady solutions, that is aligned to be force free and consequently having no velocity in the panel normal direction, places itself at the right trailing angle relative to its origin plane. The second is the piercing of two different wake systems. This would lead to numerical instabilities with a classic vortex model. Here a viscous vortex model is implemented in the presented method. Due to this vortex model it is possible to evaluate velocities next to or in the vortex core. This leads to the necessary stability to use the described method in a robust design process of the rudder including the upstream influence of the propeller.