Two-dimensional dynamic model of the interaction of a fluid and a piezoelectric bending actuator in a plane channel

Abstract

The paper proposes a two-dimensional computer model of the fluid flow in a plane channel under the action of an applied pressure drop with a flat ceramic piezoelectric actuator immersed in it, bending in the transverse direction in proportion to the applied electric voltage. A mathematical model of the coupled liquid-piezodrive system in variational form for numerical simulation by the finite element method is proposed. Since the assignment of the Dirichlet boundary conditions for displacement in this problem, is difficult, an equivalent piezo actuator deformation scheme using the Neumann boundary conditions is constructed. The deformations and equivalent stresses of von Mises on a piezo actuator are calculated. The influence of the geometry of the channel and the hydrodynamic resistance formed by the piezo actuator on the dynamics of the fluid flow is analyzed. An algorithm is proposed for adaptive dynamic remeshing of the channel computational mesh under deformations exceeding the size of finite elements. With a symmetric control signal supplied to the piezoelectric actuator, the asymmetry of the geometry leads to a violation of the symmetry of the fluid flow within the period, both in terms of fluid flow rate and in time. In the absence of a pressure drop at low frequencies of the oscillations of the piezoelectric element (of the order of the inverse relaxation time of the velocity), the period-average liquid flow rate is nonzero and increases with increasing frequency. In the presence of an external pressure drop along the layer, the average liquid flow rate is proportional to the pressure drop; at low frequencies, it is inversely proportional to the frequency; with increasing frequency, it reaches saturation. Based on the results of numerical modeling, various variants of new microfluidic technical devices generating a fluid flow using a piezoelectric bending actuator are proposed: a micropump creating a closed-circuit flow; fluid flow regulator and fluid volume dispenser.