Fluid–Structure Interaction of High Aspect-Ratio Hair-Like Micro-Structures Through Dimensional Transformation Using Lattice Boltzmann Method

Abstract

3D printed hair-like micro-structures have been previously demonstrated in a novel micro-fluidic flow sensor aimed at sensing air flows down to rates of a few milliliters per second. However, there is a lack of in-depth understanding of the structural response of these ‘micro-hairs' under a fluid flow field. This paper demonstrates the use of lattice Boltzmann methods (LBM) to understand this structural response towards a better optimization of the micro-hair flow sensors designed to suit the end applications' needs. The LBM approach was chosen as an efficient alternative to simulate Navier–Stokes equations for modeling fluid flow around complex geometries primarily for improved accuracy and simplicity with lesser computational costs. As the spatial dimensions of the sensor's flow channel are much larger in comparison to the actual micro-hairs (the sensing element), a multidimensional approach of combining two-dimensional (D2Q9) and three-dimensional (D3Q19) lattice configurations were implemented for improved computational speeds and efficiency. The drag force on the micro-hairs was estimated using the momentum-exchange method in the D3Q19 configuration and this drag force is transferred to the structural analysis model which determines the micro-hair deformation using Euler–Bernoulli beam theory. The entirety of the LBM Fluid–Structure Interaction (FSI) model was implemented within MATLAB and the obtained results are compared against the numerical model implemented on a commercially available software package.