Investigation of thrust augmentation in multi-foil flapping propulsion systems using a low-order hydrodynamic model

Tandem flapping foil propulsion is an interesting area of research with many important applications in engineering and nature. Interaction between the hindfoil and the vortex-dominated wake shed from the forefoil presents a wealth of complex unsteady flow phenomena. The spatial locations of the foils relative to each other, along with the motion parameters of the foils, determine the timing of arrival of the forefoil wake vortices at the hindfoil location and thus the outcomes of the interactions. It has been observed that some parameter combinations in a tandem arrangement can result in cycle-averaged thrust values of the hindfoil of up to two times that of isolated operation, while certain combinations can lead to significant deterioration of thrust. The parameter space involving the geometric and kinematic features of the foils and the flow properties is large and has been previously explored using experimental and high-fidelity computational approaches. In this paper, we present a low-order theoretical approach for modeling a system of multiple flapping foils using unsteady thin airfoil theory for representing the foils and a discrete-vortex method for the flowfield simulation. The predictions of the model are validated using data from the literature for three scenarios encompassing a broad range of parameters, and the simulation results are used to shed light on the thrust modification mechanism of the hindfoil in a tandem two-foil flapping system.