A Benchmark Control Problem for Supercavitating Vehicles and an Initial Investigation of Solutions

TLDR: In this article, the authors present a derivation of a benchmark problem for control of high-speed supercavitating vehicles (HSSVs) which focuses exclusively on the pitch-plane dynamics of the body.

Abstract: At very high speeds, underwater bodies develop cavitation bubbles at the trailing edges of sharp corners or from contours where adverse pressure gradients are sufficient to induce flow separation. Coupled with a properly designed cavitator at the nose of a vehicle, this natural cavitation can be augmented with gas to induce a cavity to cover nearly the entire body of the vehicle. The formation of the cavity results in a significant reduction in drag on the vehicle and these so-called high-speed supercavitating vehicles (HSSVs) naturally operate at speeds in excess of 75 m s-1. The first part of this paper presents a derivation of a benchmark problem for control of HSSVs. The benchmark problem focuses exclusively on the pitch-plane dynamics of the body which currently appear to present the most severe challenges. A vehicle model is parametrized in terms of generic parameters of body radius, body length, and body density relative to the surrounding fluid. The forebody shape is assumed to be a right cylindri...