Validation Exercises for a Free Falling Wedge Into Calm Water

This paper presents the assessment of the modelling error (Validation) of a Navier-Stokes solver using Volume of Fluid (VOF) and moving grid techniques in the simulation of a free falling wedge into calm water. This problem has been studied experimentally to determine the time histories of six pressure probes located on the wedge surface and the acceleration of the wedge. The simulation is restricted to the first 100ms after the impact of the wedge on the water (t = 0 at the impact) and the mathematical model uses the following assumptions: incompressible fluid; two-dimensional, laminar flow, negligible shear-stress at the surface of the wedge and deep water. The selected quantities of interest are the peak pressures at the six sensors, time intervals between peak pressures at the sensors, sensors pressures and acceleration of the wedge at six different time instants and integrated pressure signals for 80ms after the pressure peak at the first sensor. The application of the ASME V&V 20 standard to local quantities is presented, including the estimation of experimental and numerical uncertainties. Furthermore, a multivariate metric is used to evaluate quantitatively the overall performance of the mathematical model. The results show significant comparison errors (mismatches between simulations and measurements) for the accelerations, which may be a consequence of the assumptions of a deep water boundary condition at the bottom. However, such conclusion is hampered by some doubts about the accuracy of the experimental data. On the other hand, modeling errors are significantly smaller for the pressure measurements at the six sensors for which the main challenge is to reduce the validation uncertainty Uval. In many of the selected flow quantities, Uval is dominated by the experimental uncertainty.