Keywords: membrane pump, pumping of biological fluids, fluid-structure interaction, partitioned solution, interface quasi-Newton, mesh motion technique.

In this research, the fluid-structure interaction in a recently developed membrane pump is analysed. The rigid casing of this pump consists of a hollow circular cylinder with a height that is smaller than its radius. This casing encloses a flexible, circular membrane with a hole at its center. An electromagnet applies an oscillating motion parallel to the axis of the cylinder at the outer edge of the membrane. As a result, waves travel from the outer edge of the membrane towards its center. Hence, the fluid on both sides of the membrane is pumped from the side of the cylinder to the outlet at the center. These membrane pumps are ideally suited for biomedical applications and particle-laden flows.

The numerical simulation of such a multi-physics problem is challenging. In this research, the governing equations for the laminar flow of the incompressible fluid and the equations for the deformation of the membrane are solved with two separate codes, which are coupled with the interface quasi-Newton technique with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS) [1]. This coupling algorithm requires fewer coupling iterations per time step than dynamic relaxation techniques.

Apart from the interaction, another difficulty in the numerical simulation of these pumps is the strongly deforming fluid domain, due to the large deformation of the structure. To obtain an accurate calculation of the stress on the fluid-structure interface, the flow equations are solved in the arbitrary Lagrangian-Eulerian formulation on a deforming mesh. An innovative combination of mesh motion corresponding to the solution of Laplace equations, mesh smoothing and remeshing is used to maintain a high-quality mesh throughout the simulation.

A detailed analysis of the flow field, the deformation of the structure and the stress in the membrane is presented. An energetic analysis of the pump is performed. The mean mass flow rate supplied by the pump is 95.6g/s. The deflection of a point at the membrane's center is approximately a factor of three higher than the excitation amplitude. This large displacement restricts the excitation amplitude. The relatively large distance between the membrane and the casing of the pump entails a large backflow which consequently leads to a relatively low efficiency of 30.3%.

1

J. Degroote, K.-J. Bathe, J. Vierendeels, "Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction", Computers & Structures, 87(11-12), 793-801, 2009. doi:10.1016/j.compstruc.2008.11.013

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