Reducing the systematic error of the average fluid flow rate in axisymmetric computer model of piezoelectric micropump

Abstract

Mathematical and computer models of an axisymmetric coupled problem of interaction of a fluid and an elastic body for the solving partial differential equations by the finite element method FreeFem ++ software are proposed. In these models, periodic vibrations of annular piezoelectric actuators placed on an elastic tube of circular cross-section lead to radial deformations of the tube. With a synchronous oscillation of the system of piezoelectric actuators, the average fluid flow rate is zero. An asymmetric oscillation pattern (micropump mode) results in a nonzero average flow rate. Two types of boundary conditions are considered in the region of contact between the piezoelectric drive and the tube — Dirichlet and Neumann. The computer model was tested for unsteady fluid flow induced by a pressure gradient applied along the pipe with a circular cross section. With synchronous oscillation of piezoelectric actuators, a nonzero average fluid flow is a systematic error. This value was compared with the asymmetric oscillation pattern of piezoelectric actuators to determine the contribution of the systematic error to the pump-generated fluid flow rate. Based on the fluid flow velocity profile and the results of profiling the program code, the optimal parameters of the computational meshes for the channel (dense uniform) and tube walls (nonuniform, consistent with the velocity profile and reconstructing at each time step) were determined, which reduce the magnitude of the systematic error. The main way to reduce the error is to increase the density of the computational mesh, which leads to an increase in the required computing resources. An alternative method is proposed for reducing the systematic error due to an additional pressure drop applied to the channel. Depending on the type of boundary conditions and the number of piezoelectric actuators, this method can reduce the systematic error by 1 − 2 orders of magnitude without increasing the simulation time.