A two-dimensional analytical model of vertical water entry for asymmetric bodies with flow separation

TL;DR

This paper develops a two-dimensional analytical model for vertical water entry of asymmetric bodies with flow separation, extending Wagner's theory with the Fictitious Body Continuation to accurately estimate slamming loads.

Contribution

It extends the Fictitious Body Continuation concept to asymmetric bodies, enabling accurate predictions of water entry loads with flow separation.

Findings

FBC model reliably estimates slamming loads for asymmetric bodies.

Model matches nonlinear and CFD results for flat plates and foils.

Flow separation effects are effectively captured by the extended model.

Abstract

The vertical water entry of asymmetric two-dimensional bodies with flow separation is considered. As long as there is no flow separation, linearised Wagner's theory combined with the Modified Logvinovich Model has been shown to provide computationally fast and reliable estimates of slamming loads during water entry. Tassin et al. (2014) introduced the Fictitious Body Continuation (FBC) concept as a way to extend the use of Wagner's model to separated flow configurations, but they only considered symmetric bodies. In the present study, we investigate the ability of the FBC concept to provide accurate estimates of slamming loads for asymmetric bodies. In this case, flow separation may not occur simultaneously on both sides of the body. During an intermediate phase, slamming loads are governed by a competition between the local drop in pressure due to partial flow separation and the ongoing expansion of the wetted area. As a first benchmark for the model, we consider the water entry of an inclined flat plate and compare the FBC estimates with the results of a nonlinear model. Then, we consider the case of a foil and compare the FBC results with Computational Fluid Dynamics predictions. In both cases, we find that the FBC model is able to provide reliable estimates of the slamming loads.