Dynamics of Submersion of a «Diving Buoy» with Account of Hull Compression and Depth-Wise Variation of Water Density

Abstract

The paper employs a simplified approach to modeling of dynamics of submersion of a «diving buoy» subject to a depth-wise water density gradient and experiencing compression of the hull due to action of pressure. The latter effect is accounted for through use of well-known boiler formulae of structural mechanics allowing to analyze behavior of hulls made of different materials. Operation of a piston type buoyancy engine is modeled both for a hypothetical case of instantaneous change of buoyancy and for more practical case of finite buoyancy variation. As the analysis includes both acceleration/deceleration and constant speed modes of motion it enables to evaluate full time of submersion to a design depth. Calculated are the vertical position and speed of the vehicle versus time. Due to the fact that during submersion the growth of density results in deceleration and hull compression causes acceleration, the equilibrium condition is formulated which can be seen as hanging mode in which the buoy performs damped oscillations around a depth of hanging with a frequency depending on rates of density and compression. It is shown that to provide constant speed for a general case of density variation one has to secure a corresponding volume variation of the vehicle or a corresponding increment/decrement of differential buoyancy. At the end of the paper estimates are presented showing how much additional buoyancy should be carried on board to keep constant speed of submersion and how much power is needed for corresponding buoyancy control for a given density profile.