Wave generation for model tests

For model tests defined wave trains are generated in a model tank - preferable as deterministic wave groups at defined target locations which allows to correlate wave

excitation to structural response。 The wave generation

process can be pided into four steps:

After  summation  of  these  components,  ζl  =  。3

the preliminary instantaneous wave train at the position 1。  definition of the target wave train

2。transformation of the target wave train to the po- sition of the wave maker

3。calculation of wave maker control signal with re- gard to the characteristic RAOs of the wave maker

4。performance of model test

Definition of the target wave train

and disturbances)。 Especially when the ship is sailing at non-constant speed it is not a state of the art task to determine the wave excitation with regard to a moving reference point。

Therefore the measured wave train has to be trans- formed to a reference position of the model (both sta- tionary and moving reference frame)。 The linear calcu- lation scheme for moving models (wave in the moving reference frame of a ship) can be derived as follows:

For the definition of an appropriate target wave train different methods are available。 One procedure is to define target parameters like a typical ”Three Sisters” wave sequence Hs − 2Hs −Hs in terms of the significant

wave height Hs (Wolfram et al。 (2000))。 An optimiza- tion routine is applied to get a target wave train satis- fying the selected parameter set, see Clauss and Stein- hagen (2000)。 A target wave is also defined by full scale measurements or as output of numerical simulations。

Transformation of the target wave to the wave maker

The second step in wave generation is the transforma- tion of the given target wave train to the location of the wave maker。 This makes use of the non-linear cal- culation scheme introduced above。 Note that only the semi-empirical method allows the upstream calculation of a (non-linear) wave sequence from the target location back to the wave board。

Another approach to obtain the wave train at the wave board according to given target parameters is the com- bination of a numerical wave tank with an optimization method  (Steinhagen (2001))。

Calculation of control signals

Knowing the wave train at the wave board it is easy to calculate the appropriate control signal(s) using the different characteristic transfer functions of the wave maker (Clauss and Hennig (2003)) which allows to gen- erate the desired wave train for the model test at the target location。

Calculation of non-linear wave trains in the moving reference frame of cruising structures

For the deterministic analysis of motions and forces of ships and offshore structures the wave excitation de- notes the beginning of a complex cause reaction chain。 Dealing with a linear system the required time series are gained  from  frequency  domain  calculations。 For a non-linear system, these models become inadequate, and more sophisticated methods have to be used。 The problem gets even more complex when the structure is moving at constant or non-constant speed, as stationary measurements in a model tank do not provide the wave train at the position of the investigated model in the moving reference frame of a cruising ship。 Wave probes can be installed at defined positions, but usually not at the position of the model (due to relative motions

where  6xi  stands  for  the  time  varying  distance be-

tween both locations。 Considering the non-linear kj and the adequate F (ωj, xl) from the empirical-analytical ap- proach the wave train has to be calculated at the posi- tion of the model reference point x(ti) at each time step in order to get the non-linear moving reference frame wave train。