Validation of a numerical wave tank based on a RANSE solver

The second numerical wave tank presented here is set up using the commercial state of the art CFD solver FLU- ENT (Fluent (2003))。 For all flows, FLUENT  solves the conservation equations for mass and momentum (Navier-Stokes equations)。 For simulating the free sur- face the Volume of Fluid method (VOF) is used which can deal with wave breaking phenomena。 For simu- lating the wave board motion of the piston type wave generator a dynamic mesh approach (dynamic layering) is introduced。 The motion of the wave board is simu- lated by moving the boundary forwards and backwards like the wave board in the experiment。 Therefore, cells have to be added to or deleted from the fluid domain as the size of the calculation domain changes with time。 Further details on the numerical wave tank are given in Clauss et al。 (2004a)。

Fig。 9 presents the comparison between calculations and measurement of a wave packet with a JONSWAP spec- trum at different positions in the wave tank (tank di- mensions: length 80 m, width 4 m, water depth 1。5 m, piston type wave generator)。 It can easily be seen, that the phases and amplitudes are well predicted by the nu- merical wave tank。 Wave packets can e。g。 be used to simulate extreme waves (Ku¨hnlein et al。 (2002)) or to model high wave groups within a natural sea state like in Fig。 10: It shows the simulation of the wave packet from Fig。 9 integrated to irregular seas。

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As a RANSE solver is used for this wave tank the du- ration of the calculation is significantly higher as com- pared to the numerical wave tank based on potential theory and FEM。 To make use of the benefits of both methods a combined approach is recommended: poten- tial theory as long as no wave breaking occurs, and

Target wave train (New Year Wave)

Wave maker control signal

Fig。 9: Simulation of a wave packet (Hmax = 0。35 m) based on RANSE/ VOF in comparison to measurement (same JONSWAP spectrum as in Fig。 10)。 Generation of the wave maker control signal for both model tank and numerical wave tank data using the modified the- ory。

Fig。 8: Generation and analysis of the New Year Wave: applying the modified non-linear approach the target wave train (top) is transformed upstream to the position of the wave maker。 The resulting control signal is shown here (second graph)。 Both the modified theory and the numerical wave tank based on potential theory are able to calculate the downstream wave train at the target position — the numerical tank only from the control signal which is provided by the modified theory。 The corresponding wave field characteristics are provided by the numerical wave tank (scale 1:81)。

RANSE code if breaking is encountered。

Both numerical wave tanks are not capable to transform a given wave train backwards to the position of the wave generator。 In order to generate a predetermined wave sequence at a target location the numerical wave tank has to be combined with the modified approach or op- timization routines (Clauss and Steinhagen (2000))。

Experimental investigation of offshore structures

For the experimental investigation of wave-structure in- teraction of stationary offshore structures it is impor- tant to know the exact wave train at the model posi-

Fig。  10:  Irregular  sea  (JONSWAP  spectrum,  TP =

4。2 s,  Hs  =  0。1  m)  with  integrated  wave packet (Hmax = 0。35 m) at different positions in the wave tank。 Numerical simulation based on RANSE/ VOF。 Gener- ation of the wave maker control signal for both model tank and numerical wave tank data using the modified theory。

tion。 Measurements close to the model are disturbed by radiation and diffraction。 Using the presented modified non-linear approach the wave train can be calculated at any position of the model tank。