Simulation of Fluid Flow through a Elastic Microchannel Deformed by a Piezoelement in Microgrip Cooling Systems

The flow of the fluid in an elastic cylindrical microchannel, the central part of which is located inside the piezoelectric ring, is simulated numerically. It arises as due to channel deformation by piezoelement according to the harmonic law, and pressure drop at the inlet and outlet to the microchannel. The aim of the work is to create a three-dimensional computer model of controlling the flow of a fluid by means of a pressure drop and a tube compression piezoelectric element. The model of an element of a computational bench that allows you to find fluid flow using specified analytical formulas, built using an approximation of the calculation results for the full model for individual sets of parameters. Modeling an element of a computing bench will allow real-time calculations with direct integration into the control system of a technical device. The model is based on the obtained analytical dependencies taking into account the restrictions introduced, which can significantly reduce the amount of computation and improve the quality of the result. The solution of the full equations of elasticity for the tube and the equations of hydrodynamics in the microchannel was carried out numerically by the finite element method in the package of numerical simulation FreeFem++. Numerical results are obtained for the flow rate of a fluid as a function of time, the physical properties of the fluid (dynamic viscosity and density) and external influences (the magnitude of the pressure gradient, the amplitude and frequency of compression of the piezoelectric element). The variants of using the obtained results in practical applications are shown. For example, in a liquid cooling system, the obtained relationship between the system parameters allows one to determine the flow regime that prevents the flow of heated liquid through the channel outlet. It is planned to use the results in the development of a computing stand for capillary micro-capture, containing two tubes (at the input and output) with piezoelectric elements, dividing the device into two parts (with dynamically changing and unchanged geometries) which will greatly simplify the full simulation.

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