Shallow water entry modeling and experiments

Authors: Mohammad Jalalisendi Sam Zhao Maurizio Porfiri

Publish Date: 2016/10/18

Volume: 104, Issue: 1, Pages: 131-156

PDF Link

Abstract

As marine vessels expand their range of operations and their planing speeds increase understanding the physics of shallow water entry becomes of paramount importance Highspeed impact on the surface is responsible for impulsive hydrodynamic loading spatiotemporal evolution of which is controlled by the entry speed and the vessel geometry For shallow water impact the presence of the ground may further influence the hydrodynamic loading by constraining the water motion beneath the impacting hull Here we present a theoretical and experimental framework to investigate shallow water entry in the context of the twodimensional water impact of a wedge Wagner theory is extended to describe the finiteness of the water column and the resulting mixed boundary value problem is analytically solved to determine the velocity potential free surface elevation and pressure field To complement and validate the semianalytical scheme experiments are performed using particle image velocimetry by systematically varying the height of the water column The velocity data are then utilized to reconstruct the pressure field in the fluid and infer the hydrodynamic loading on the wedge Experimental observations confirm the accuracy of the proposed modeling framework which is successful in anticipating the role of the bottom wall on the physics of the impact Our results indicate that the pressure distribution is controlled by the water height whereby we observe an increase in the pressure at the keel accompanied by a decrease in the pileup as the water column becomes thinner The results of this study are expected to offer insight into the design of marine vessels and constitute a solid basis for understanding the role of fluid confinement in shallow water entryThis work has been supported by the Office of Naval Research with Dr Y D S Rajapakse as the program manager Grant N000141010988 and the Mitsui USA Foundation The authors would like to thank Dr M G Iskander for kindly providing the highspeed camera for the purpose of this study Finally the authors would like to thank Mrs F Cellini V Mwaffo and A Shams for help in revising the first draft of this work Views expressed herein are those of the authors and not of the funding agencyComparison between entry depth xi obtained from keel tracking black lines and position sensor blue lines for a h=10 cm b h=75 cm c h=5 cm and d h=25 cm Solid dashed and dashdotted lines correspond to the three repetitions Color figure onlineComparison between entry speed dotxi data obtained from differentiating tracked displacement data black lines or integrating the acceleration blue lines for a h=10 cm b h=75 cm c h=5 cm and d h=25 cm Solid and dashdotted lines correspond to the two repetitionsTo ascertain accuracy of the entry speed obtained by integrating the acceleration we perform an extra set of experiments where the setup is modified to focus only on tracking the movement of the wedge from the onset of the fall until it is entirely submerged in the water column Toward this aim a Phantom camera V91 at an acquisition rate of 4mathrm kHz and resolution of 688times 552mathrm pixels is focused on the sledge To ease the tracking an extra light is utilized to illuminate six points drawn on the sledge which are tracked using Xcitex ProAnalyst These data are averaged to obtain the entry depth xi in each trial and two repetitions are performed for each water column height The entry velocity is calculated by differentiating the entry depth using the “gradient” function in MATLAB Figure 16 compares the entry speed obtained from tracking with accelerometer data Despite the oscillations in the tracked data we find good agreement between the two methods

Keywords: