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Computational studies of resonance wave pumping in compliant tubes. (English) Zbl 1145.76355
Summary: The valveless impedance pump is a simple design that allows the producion or amplification of a flow without the requirement for valves or impellers. It is based on fluid-filled flexible tubing, connected to tubing of different impedances. Pumping is achieved by a periodic excitation at an off-centre position relative to the tube ends. This paper presents a comprehensive study of the fluid and structural dynamics in an impedance pump model using numerical simulations. An axisymmetric finite-element model of both the fluid and solid domains is used with direct coupling at the interface. By examining a wide range of parameters, the pump’s resonance nature is described and the concept of resonance wave pumping is discussed. The main driving mechanism of the flow in the tube is the reflection of waves at the tube boundary and the wave dynamics in the passive tube. This concept is supported by three different analyses: (i) time-dependent pressure and flow wave dynamics along the tube, (ii) calculations of pressure-flow loop areas along the passive tube for a description of energy conversion, and (iii) an integral description of total work done by the pump on the fluid. It is shown that at some frequencies, the energy given to the system by the excitation is converted by the elastic tube to kinetic energy at the tube outlet, resulting in an efficient pumping mechanism and thus significantly higher flow rate. It is also shown that pumping can be achieved with any impedance mismatch at one boundary and that the outlet configuration does not necessarily need to be a tube.

##### MSC:
 76D33 Waves for incompressible viscous fluids 76M10 Finite element methods applied to problems in fluid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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