Drag cancellation by added-mass pumping

TL;DR

This paper investigates how periodic shape changes in submerged bodies can cancel viscous damping through added-mass energy recovery, enabling sustained oscillations and informing design of shape-changing underwater vehicles.

Contribution

It introduces an analytical model and simulation study demonstrating how added-mass recovery can cancel damping and sustain oscillations in shape-changing submerged bodies.

Findings

Added-mass recovery can fully cancel viscous damping.

Sustained oscillations with amplitudes up to four times body radius.

Optimal pumping frequency range identified for oscillation sustainability.

Abstract

A submerged body subject to a sudden shape-change experiences large forces due to the variation of added-mass energy. While this phenomenon has been studied for single actuation events, application to sustained propulsion requires studying \textit{periodic} shape-change. We do so in this work by investigating a spring-mass oscillator submerged in quiescent fluid subject to periodic changes in its volume. We develop an analytical model to investigate the relationship between added-mass variation and viscous damping and demonstrate its range of application with fully coupled fluid-solid Navier-Stokes simulations at large Stokes number. Our results demonstrate that the recovery of added-mass kinetic energy can be used to completely cancel the viscous damping of the fluid, driving the onset of sustained oscillations with amplitudes as large as four times the average body radius $r_0$. A quasi-linear relationship is found to link the terminal amplitude of the oscillations $X$, to the extent of size change $a$, with $X/a$ peaking at values from 4 to 4.75 depending on the details of the shape-change kinematics. In addition, it is found that pumping in the frequency range of $1-\frac{a}{2r_0}<\omega^2/\omega_n^2<1+\frac{a}{2r_0}$ is required for sustained oscillations. The results of this analysis shed light on the role of added-mass recovery in the context of shape-changing bodies and biologically-inspired underwater vehicles.