Keywords: piezofan, fluid-structure interaction, partitioned solution, IQN-ILS, optimization, heat fins.

In this paper, the heat transfer from a single heat fin to the air flow in the wake of a piezoelectric fan (piezofan) is optimised. A bimorph piezofan consists of a thin, passive plate which is clamped at one end. The top and bottom of this plate are partially covered by a thin patch of piezoelectric material. By applying alternating voltages with a phase shift of 180 degrees to the patches, one of the patches expands in the direction parallel to the plate while the other one contracts in that same direction. Due to these small but opposite deformations of the patches on its top and bottom, the elastic plate bends, resulting in a significant motion of the free end. If the excitation frequency is close to the resonance frequency of the plate, the oscillation amplitude is relatively large. The interaction between the piezofan and the surrounding air induces an air flow from the clamped end towards the free end. Consequently, a piezofan can be used to cool electronic components. Piezofans are an alternative to conventional rotating fans as their power consumption is an order of magnitude smaller.

The numerical simulation of a piezofan is challenging. In this work, the governing equations for the flow of and the heat transfer in the incompressible fluid and the equations for the deformation of the piezofan 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]. Apart from the interaction, another difficulty in the numerical simulation of a piezofan is the strongly deforming fluid domain, due to the large deformation of the structure. Therefore, the flow equations are solved in the arbitrary Lagrangian-Eulerian formulation on a deforming mesh.

With the fluid-structure interaction model, a number simulations are performed simultaneously on different cluster nodes, each with a different excitation frequency applied to the piezoelectric patches. Afterwards, the time-averaged heat transfer is calculated for each frequency. Then, a cubic spline surrogate model is constructed through these data points. The optimization with the heat transfer as an objective and the frequency as design variable is subsequently performed using the surrogate model, instead of using the actual model. The result of the optimization process is close to the first eigenfrequency of the structure.

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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