Piezoelectric energy harvests by the usage of a laminar pulsating flow circulating in a rectangular channel

Abstract This work develops a theoretical study of a piezoelectric energy harvester, perturbed through a fully developed laminar flow with an oscillating pressure gradient. Considering a fully developed hydrodynamic flow, the electric energy generated in the piezoelectric element is due only to shear stresses yielded at the inner surfaces of the channel. In this manner, a fraction of the viscous forces is converted into unitary deformations at the piezoelectric, and the other fraction is transformed to induced electric piezoelectric energy. Using dimensionless analysis, the formulation of resulting dimensionless governing equations for the fluid and the corresponding deformation and electric potential fields for the piezoelectric material constitute a conjugate problem, solved by considering harmonic solutions. Although the dimensionless power output is a multi-parametric function, due to the large number of dimensionless parameters involved, we find that the main behavior of the electrical power depends very sensitively on two fundamental dimensionless parameters: the Womersley number, α , associated with the oscillating flow and a parameter that measures the physical importance of the electrical energy produced by the action of the velocity field. For the first case, it is seen that the power increases if the Womersley number is decreased while for the second case, the inverse behavior is predicted. Therefore, there is a clear operation of the physical system for which better conditions can be reached by selecting and varying appropriately the assumed values of different dimensionless parameters.