On modeling added mass and circulation terms with fast potential-flow methods for oscillating-foil propulsors

The design of cycloidal thrusters and other oscillating foil propulsors requires fast tools that provide accurate estimates of propulsor hydrodynamic performance and mechanical loads. Potential-flow theory coupled with empirical formulae that account for viscous effects is the best choice for fast multi-parameter optimization. Within this context, oscillating foils are usually approximated as thin wings with flow solutions derived from small-disturbance theory. Added mass (non-circulatory) effects may be relevant even under such assumptions. They can be easily included in the flow equations assuming that the foil is a flat plate heaving and pitching. However, for blade motions involving complex trajectories like those in Voith Schneider propellers, the foils describe cycloidal loops, and the assumption of small pitch angles is no longer valid. Therefore, a more accurate modeling of added mass and circulatory terms is required. This paper presents extensions to a previous model, which allows for a more precise representation of the added mass terms in the potential flow equations, combining low computational cost and accurate modeling. The results show clear improvement in the evolution foil forces in time when the new approach is used. The extensions are especially needed for the simulations of foils describing complex paths with large variations of pitch angle. Applications to transverse-axis cycloidal propulsors are presented as well as to unconventional counter-flapping propulsors that have recently appeared in the scientific literature. Validation of the method with RANS computations is provided.